Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
5th Edition
ISBN: 9780321816252
Author: C. Henry Edwards, David E. Penney, David Calvis
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 2.6, Problem 18P
Program Plan Intro
Use Range-Kutta method twice to approximate (to five decimal places) this solution on given interval, first with step size h=0.2, h=0.1, h=0.05 and h=0.025. Make the table showing the approximate values and the actual value.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. (The weight-density of water is 62.4 pounds per cubic foot. Round your answer to
two decimal places.)
Parabola, y = x²
Ib
Submit Answer
The circular rod shown is made of the steel alloy AISI 4140 OQT 900. It has a diameter of
1.00 in and an initial length of 48 in. An axial tensile load of 15 000 lb. is applied during a
certain operation.
Compute:
1. the equivalent spring constant K,
2. the deformation X of the rod.
The Young's modulus of the steel is known to be 30,000,000 psi.
F=15 000 lb
L= 48 in
F=15 000 lb
Numerical Methods Lecture:
The system of nonlinear equations given below x0 =y0=1 Obtain 4 iteration Newton-Raphson solutions starting with the estimated initial values.Discuss the digit precision in the accuracy of the final solutions.
x = y+x2-0.5
y = x2-5xy
Chapter 2 Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
Ch. 2.1 - Prob. 1PCh. 2.1 - Prob. 2PCh. 2.1 - Prob. 3PCh. 2.1 - Prob. 4PCh. 2.1 - Prob. 5PCh. 2.1 - Prob. 6PCh. 2.1 - Prob. 7PCh. 2.1 - Prob. 8PCh. 2.1 - Prob. 9PCh. 2.1 - Prob. 10P
Ch. 2.1 - Prob. 11PCh. 2.1 - Prob. 12PCh. 2.1 - Prob. 13PCh. 2.1 - Prob. 14PCh. 2.1 - Prob. 15PCh. 2.1 - Prob. 16PCh. 2.1 - Prob. 17PCh. 2.1 - Prob. 18PCh. 2.1 - Prob. 19PCh. 2.1 - Prob. 20PCh. 2.1 - Prob. 21PCh. 2.1 - Suppose that at time t=0, half of a logistic...Ch. 2.1 - Prob. 23PCh. 2.1 - Prob. 24PCh. 2.1 - Prob. 25PCh. 2.1 - Prob. 26PCh. 2.1 - Prob. 27PCh. 2.1 - Prob. 28PCh. 2.1 - Prob. 29PCh. 2.1 - A tumor may be regarded as a population of...Ch. 2.1 - Prob. 31PCh. 2.1 - Prob. 32PCh. 2.1 - Prob. 33PCh. 2.1 - Prob. 34PCh. 2.1 - Prob. 35PCh. 2.1 - Prob. 36PCh. 2.1 - Prob. 37PCh. 2.1 - Fit the logistic equation to the actual U.S....Ch. 2.1 - Prob. 39PCh. 2.2 - Prob. 1PCh. 2.2 - Prob. 2PCh. 2.2 - Prob. 3PCh. 2.2 - Prob. 4PCh. 2.2 - Prob. 5PCh. 2.2 - Prob. 6PCh. 2.2 - Prob. 7PCh. 2.2 - Prob. 8PCh. 2.2 - Prob. 9PCh. 2.2 - Prob. 10PCh. 2.2 - Prob. 11PCh. 2.2 - Prob. 12PCh. 2.2 - Prob. 13PCh. 2.2 - Prob. 14PCh. 2.2 - Prob. 15PCh. 2.2 - Prob. 16PCh. 2.2 - Prob. 17PCh. 2.2 - Prob. 18PCh. 2.2 - Prob. 19PCh. 2.2 - Prob. 20PCh. 2.2 - Prob. 21PCh. 2.2 - Prob. 22PCh. 2.2 - Prob. 23PCh. 2.2 - Prob. 24PCh. 2.2 - Use the alternatives forms...Ch. 2.2 - Prob. 26PCh. 2.2 - Prob. 27PCh. 2.2 - Prob. 28PCh. 2.2 - Consider the two differentiable equation...Ch. 2.3 - The acceleration of a Maserati is proportional to...Ch. 2.3 - Prob. 2PCh. 2.3 - Prob. 3PCh. 2.3 - Prob. 4PCh. 2.3 - Prob. 5PCh. 2.3 - Prob. 6PCh. 2.3 - Prob. 7PCh. 2.3 - Prob. 8PCh. 2.3 - A motorboat weighs 32,000 lb and its motor...Ch. 2.3 - A woman bails out of an airplane at an altitude of...Ch. 2.3 - According to a newspaper account, a paratrooper...Ch. 2.3 - Prob. 12PCh. 2.3 - Prob. 13PCh. 2.3 - Prob. 14PCh. 2.3 - Prob. 15PCh. 2.3 - Prob. 16PCh. 2.3 - Prob. 17PCh. 2.3 - Prob. 18PCh. 2.3 - Prob. 19PCh. 2.3 - Prob. 20PCh. 2.3 - Prob. 21PCh. 2.3 - Suppose that =0.075 (in fps units, with g=32ft/s2...Ch. 2.3 - Prob. 23PCh. 2.3 - The mass of the sun is 329,320 times that of the...Ch. 2.3 - Prob. 25PCh. 2.3 - Suppose that you are stranded—your rocket engine...Ch. 2.3 - Prob. 27PCh. 2.3 - (a) Suppose that a body is dropped (0=0) from a...Ch. 2.3 - Prob. 29PCh. 2.3 - Prob. 30PCh. 2.4 - Prob. 1PCh. 2.4 - Prob. 2PCh. 2.4 - Prob. 3PCh. 2.4 - Prob. 4PCh. 2.4 - Prob. 5PCh. 2.4 - Prob. 6PCh. 2.4 - Prob. 7PCh. 2.4 - Prob. 8PCh. 2.4 - Prob. 9PCh. 2.4 - Prob. 10PCh. 2.4 - Prob. 11PCh. 2.4 - Prob. 12PCh. 2.4 - Prob. 13PCh. 2.4 - Prob. 14PCh. 2.4 - Prob. 15PCh. 2.4 - Prob. 16PCh. 2.4 - Prob. 17PCh. 2.4 - Prob. 18PCh. 2.4 - Prob. 19PCh. 2.4 - Prob. 20PCh. 2.4 - Prob. 21PCh. 2.4 - Prob. 22PCh. 2.4 - Prob. 23PCh. 2.4 - Prob. 24PCh. 2.4 - Prob. 25PCh. 2.4 - Prob. 26PCh. 2.4 - Prob. 27PCh. 2.4 - Prob. 28PCh. 2.4 - Prob. 29PCh. 2.4 - Prob. 30PCh. 2.4 - Prob. 31PCh. 2.5 - Prob. 1PCh. 2.5 - Prob. 2PCh. 2.5 - Prob. 3PCh. 2.5 - Prob. 4PCh. 2.5 - Prob. 5PCh. 2.5 - Prob. 6PCh. 2.5 - Prob. 7PCh. 2.5 - Prob. 8PCh. 2.5 - Prob. 9PCh. 2.5 - Prob. 10PCh. 2.5 - Prob. 11PCh. 2.5 - Prob. 12PCh. 2.5 - Prob. 13PCh. 2.5 - Prob. 14PCh. 2.5 - Prob. 15PCh. 2.5 - Prob. 16PCh. 2.5 - Prob. 17PCh. 2.5 - Prob. 18PCh. 2.5 - Prob. 19PCh. 2.5 - Prob. 20PCh. 2.5 - Prob. 21PCh. 2.5 - Prob. 22PCh. 2.5 - Prob. 23PCh. 2.5 - Prob. 24PCh. 2.5 - Prob. 25PCh. 2.5 - Prob. 26PCh. 2.5 - Prob. 27PCh. 2.5 - Prob. 28PCh. 2.5 - Prob. 29PCh. 2.5 - Prob. 30PCh. 2.6 - Prob. 1PCh. 2.6 - Prob. 2PCh. 2.6 - Prob. 3PCh. 2.6 - Prob. 4PCh. 2.6 - Prob. 5PCh. 2.6 - Prob. 6PCh. 2.6 - Prob. 7PCh. 2.6 - Prob. 8PCh. 2.6 - Prob. 9PCh. 2.6 - Prob. 10PCh. 2.6 - Prob. 11PCh. 2.6 - Prob. 12PCh. 2.6 - Prob. 13PCh. 2.6 - Prob. 14PCh. 2.6 - Prob. 15PCh. 2.6 - Prob. 16PCh. 2.6 - Prob. 17PCh. 2.6 - Prob. 18PCh. 2.6 - Prob. 19PCh. 2.6 - Prob. 20PCh. 2.6 - Prob. 21PCh. 2.6 - Prob. 22PCh. 2.6 - Prob. 23PCh. 2.6 - Prob. 24PCh. 2.6 - Prob. 25PCh. 2.6 - Prob. 26PCh. 2.6 - Prob. 27PCh. 2.6 - Prob. 28PCh. 2.6 - Prob. 29PCh. 2.6 - Prob. 30P
Knowledge Booster
Similar questions
- a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a. f(x) = 2x°, a = 1 %3D ..... a. f'(a) =arrow_forwardSuppose that a parachutist with linear drag (m=50 kg, c=12.5kg/s) jumps from an airplane flying at an altitude of a kilometer with a horizontal velocity of 220 m/s relative to the ground. a) Write a system of four differential equations for x,y,vx=dx/dt and vy=dy/dt. b) If theinitial horizontal position is defined as x=0, use Euler’s methods with t=0.4 s to compute the jumper’s position over the first 40 s. c) Develop plots of y versus t and y versus x. Use the plot to graphically estimate when and where the jumper would hit the ground if the chute failed to open.arrow_forwardUse matlab In Problems 5-10 use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h 5 0.1 and then use h 5 0.05. 8. y'=xy+ sqrt(y), y(0)=1, y(0.5) I tried this method, but it gives me errors "un recongnized function or variable at 'xy'. Error in live 5 and error in line 17 close all clear clc f=@(x,y) xy+sqrty; % Given ODE x0=0; xf=0.5; % Interals of x y0=1; % Intital condition h1-0.1; % Step Size 1 y1=euler (x0, yo, xf, h¹, f); fprintf('For h=0.1, y(0.5) - %.4f/n', y1(end)) y2=euler (x0, yo, xf, h2, f); fprintf('For h=0.05, y(0.5)=%.4f/n', y2(end)) function y=euler (x0, yo, xf, h, f) y(1)=y0; x-x0:h:xf; for i=1:length(x) -1 f1-f(x(i), y(i)); y(i+1)=y(i)+h*f1; %Euler's Update end endarrow_forward
- For an object of mass m=3 kg to slide without friction up the rise of height h=1 m shown, it must have a minimum initial kinetic energy (in J) of: h O a. 40 O b. 20 O c. 30 O d. 10arrow_forwardDetermine the drag coefficient c needed for a parachutist of mass m=68.1kg to have a velocity of 40m/s after free-falling for time t=10s. Note: The acceleration due to gravity is 9.8m/s2. Use the Regula Falsi methodarrow_forwardDiscuss the requirement for numerical approximation of various equation solutions.arrow_forward
- An aluminum wire having a cross-sectional area equal to 4.60 x 10-6 m? carries a current of 7.50 A. The density of aluminum is 2.70 g/cm³. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire. 1.95E-4 The equation for the drift velocity includes the number of charge carriers per volume, which in this case is equal to the number of atoms per volume. How do you calculate that if you know the density and the atomic weight of aluminum? mm/sarrow_forwardA vertical plate is partially submerged in water and has the indicated shape. 4 m 12 m- Express the hydrostatic force (in N) Enter a number. He of the plate as an integral (let the positive direction be upwards) and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s for the acceleration due to gravity. Recall that the weight density of water is 1,000 kg/m3.) pg dy = Narrow_forwardA 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5 pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5 gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows. Q' (t) = = (b) Find the quantity of salt in the tank as it's about to overflow. esc C ✓ % 1 1 a 2 W S # 3 e d $ 4 f 5 rt 99 6 y & 7 h O u * 00 8 O 1 9 1 Oarrow_forward
- M D d T M. P- A circular shaft having diameters D and d and a groove of radius r (with M = 0 and P O) is made of steel with the allowable shear stress tall. Find the maximum torque I that can be transmitted by the shaft. Given: D = 28mm, d = 20mm, r = 4mm, and tall = 250 MPa. Please help with this question. The answer should be 157.1 Nmarrow_forwardA fish is swimming north at 1.2 m/s. It then undergoes an average acceleration of 8.3 m/s^2 51 degrees south of west for 0.25 s. What is the magnitude of the fish's final velocity. Please include a drawingarrow_forward1.) The distribution of I & Q is zero-mean Gaussian; their phase, amplitude, and power are uniform, Rayleigh, and Exponential distribution. Using the given I & Q data to show these distributions. Requirements: In this project, please use the I & Q data from 1000 gate to demonstrate these PDFS. Data from azimuthal angle between 5° to 30°, range between 20 km to 50 km are suggested used in this analysis.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr
C++ for Engineers and Scientists
Computer Science
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Course Technology Ptr