Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O sec5х + tan5x O None

Q: (2y – 3x)dx +xdy = 0 %3D

A: Find your answer below

Q: Determine the integrating factor of the Bernoulli's equation given pelow: dy -y cot2x = y' csc2x dx…

A: ................(1) substitute take derivative .................put it back in equation 1

Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: The integration of ſ, Vx tan-'Vx dx is

A: Given that  The integral is

Q: dw Use the Chain Rule to find where w = cos 8x sin 2y, x = and y = t*. dt 4' dw II

A: w=cos8x sin2y  , x=t4 and y=t4 dxdt=dt4dt=14 dydt=dt4dt=4t3   ∂w∂x=8 cos8x cos2y ∂w∂y=sin8x -2 sin2y…

Q: Find dz/dx and dz/dy for: x² sin (y³) + xe32 – cos(z²) = 3y – 6z + 8

A: Here, the given equation is: x2sin(y3)+xe3z-cos(z2)=3y-6z+8...(1) So, z is a function of x and y

Q: Integrate by Substitution. 1. dx where u = Vx+2 2Vx+2

A: By using substitution method, we calculate the given integral.

Q: use Separation of Variables to find the general solution. dy/dt= y tan t

A:

Q: To evaluate fx (cos x2)e* dx, use integration by parts. What is the best choice for u and du?

A: Consider the provided integral, ∫ xcosx2ex2dx Evaluate the provided integral. Apply the substitution…

Q: Find the differential dy of the given function. y sec² x x² + 2 dy sec²x(x²+2)tan x-x (x² + 2)² dx X

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Q: Find the integration Sx cos 2x dx

A: Here we have to use integration by parts to find the answer.

Q: find dy>dt.                                                        y = cos4 (sec2 3t)

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Q: The integrating factor of the LDE y'=x-2ycotx is A B с D sin²x sec²x csc²x cos²x

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Q: Find dy/dt of y = Ssin (cost) and simpli -t -cos t cos t V1-? the

A: Given:- y=sin(cos-1(t))  To find:- y'

Q: Use the Chain Rule to find dz where z = 2x cos y, x=t, and y = 5t. dt dz dt (Type an expression…

A:

Q: Integrate the function. 8 dx V36 - 64x2 X+ C sin-1 + C -1 + C D 4 tan-1 3. B

A: Given:       ∫836-64x2dx  substitute u=4x3→dudx=43                   dx=34du         =∫636-36u2du…

Q: :Use variation of parameters to solve dx Зх — Зу + 4 dt dy 3D 2х — 2у — 1 dt

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Q: Find dydx? for f(x, y) = eXy

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Q: integrate by parts t7 sin⁡(2t4 )dt

A: We have given indefinite integration with respect to x. While solving the indefinite integral, we…

Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, 4t2), o sts 1. (Round your answer to…

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Q: Find DE using variable separable cos/dx + 1/ydy=0

A: Given that: cosxdx+1ydy=0

Q: 2 ydx -3ху-dx — хӑу — 0 xdy = 0

A:

Q: Find the Integrating Factor of dy OY + 2ytanx = sinx dx O a. sec?x O b. secxtanx O c. secx O d.…

A: Given, dydx+2ytanx=sinx....1 Comparing the given equation with the equation, dydx+Py=Q We get,…

Q: e ln (xle) (2– sec²r)cm#/c°sec³x sec(3A – x) What should be the value of A for -dx to be integrable…

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Q: Find the length of the curve y = V cos 2t dt from x= 0 to x = 4

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Q: Evaluate using Integration by parts. ∫e4x cos(2x)dx

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Q: Solve the equation using suggested substitution: (3siny-5x)dx + 2x2cotydy = 0; let z = siny

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Q: solve: d/dx on the intergral 2x to x3 with an integrand of t2 et^5 dt

A: Given integral is

Q: Use the Chain Rule to find dw/dt. w = In Vx2 + y2 + z2 x = 2 sin(t), y = 5 cos(t), z = 4 tan(t) dw…

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Q: Obtain the integrating factor of the non-exact DE, (2 + ycosx)dx + xcosxdy = 0. a. secx b. cosx c…

A: Integrating factor

Q: find dyldx for the flowing * y = secʻx – tan“ x Î Add File y = 3 sin' 2. 1 Add File ) y = x.sinh2x…

A: Explanation of the answer is as follows

Q: Find the differential dy of the given function. y sec² x x² +2 dy = sec²x(x²+2)tan x-x (x²+2)² dx x

A:

Q: Integrate by parts (3t+t2)sin(2t)dt

A: Formula for integration by parts where f and g are 2 different parts             f' and g' are…

Q: dz Use the Chain Rule to find dt for z = x? + y? + xy, x = sin t, y = et.

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Q: dx 5 + 4 sin a

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Q: Q3: Find if: dx 2x dt sinx dt (1) y = (2) y = [ %3D t- 2 X cosx

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Q: se the Chain Rule to find dw/dt. w = INVX2 + y2 + z² x = 9 sin(t

A: Here we have to use the chain rule to find dwdt=? w=lnx2+y2+z2, x=9sin(t), y=3cos(t), z=5tan(t)

Q: Use the Chain Rule to find dz/dt.z = sqt(8+x^2+y^2,    x = 4 ln t,    y = cos t dz/dt=

A: Please refer to the image below

Q: Find / tan- -dx using integration bv parts. TM

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Q: Apply integration by parts: S udv - S vdu = uV sin2x – cos2x dx sin2x + cos2x

A: Given function is sin 2x-cos 2xsin 2x+cos 2x. Integrate using integration by parts. Chain rule of…

Q: Use differentiation rules to find y' = dy/dx.

A: Given,

Q: Q10.a) Find rsinx if tnx Jt +5 dt + siny = x – x²cosy

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Q: Test for homogeneity

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Q: 3 3 У(х'у + 2х — у)dx + x (ху — 2) dy 3D 0 3

A: Firstly we find Integrating factor, then find general solution.

Q: ds Find where Vt +s = 2s . %3D dt

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Q: Find the intergral of  (t^2 sin(t)cos(t) +t sin^2 (t) )dt

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Q: Find the integrating factor μ(x) of y' + 4y - tan(x) = 0 such that μ(0) = 1. μ(x) =

A: See the details solution in below

Q: Find where) i ) et u*rany tany = 1 , U= xInx (use chatn reule ) ii) coscxy) - * + e+y) = 2 yz

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.