6. Find all real solutions to V3x +1+ V9x + 4 = 11. Show your work!

Q: Prove that there are no integer solutions (x, y, z, w) to the equation x³ +y³ 3z²+9w² +3. =

A: The given equation is x3+y3=3z2+9w2+3. We have to prove that there is no integer solution to the…

Q: Find the complete solution of (x + 4y³dy – ydx = 0)

A:

Q: Show that r: y = 3. 2n

A: Using two sectant theorem,  ∠n=12x-y  Multiply both sides by 2. ⇒2n=x-y .....(1) Using intersecting…

Q: Verica didn't solve this radical equation correctly. Here is their work: U2x-2 = x- I %3D ©…

A: We have to solve the radical equation 2x-2=x-1.

Q: Use the IVT to prove that r-5x2 + 2x = -1 has a solution. %3D

A:

Q: Use the Gauss-Seidel iterative technique to find approximate solutions to 10x1 – x2 + 2x3 = 6, -x1 +…

A:

Q: Exercise 5 Find a (real) general solution. Show each step of your work. y" + 5y/ + 4y = 10e-

A: 5) → Given differential equation is          y" + 5y' + 4y = 10e-3xFirst find the complementory…

Q: П. Solve xау + (3х 2y)ax = U in two ways

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Q: xdx can be solved by either algebraic subsitution or integrataion by parts. X-1 A True False

A: We have to state whether the given statement is true or false and its reason is given.

Q: wouldn't there be a t in the second term of the general solution?

A:

Q: Find all solutions of x2 - x + 2 = 0 over Z3[i].

A: Given: Z3i=a+bi|a,b∈Z3       =0, 1, 2, i, 1+i, 2+i, 2i, 1+2i, 2+2i We have to find all solutions for…

Q: 2. Determine the complete solution of xydy – (x + 2y)²dy = 0 %3D

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Q: Find the number of solutions to 6z1+9z2+20z3=150 where the zi are nonnegative integers.

A:

Q: state where in the ty-plane the hypotheses of Theorem are satisfied 7. y′=(t2+y2)3/2

A: Given y'=t2+y232

Q: Find all the separable solutions to the equation 0 0 и, (0, г) %— и,(1,1) 3 0, г>0. Ин — ихх + и…

A: In the given question we have to find the solution of the given non homogenuous wave equation s.t…

Q: A) (:: :) Verify that y = c₁cos(3x) + c₂sin(3x) is a solution of y' +9y = 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Prove that the equation 3x² – 3x + 2 = 0 has a solution on interval [0; 1].

A:

Q: 9. Find the general solutions of X' = AX with A =

A:

Q: 4- Find the particular solution for: 3x²y' = 5x – 6xy, x = 2 when y = 1 %3D

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Q: Find general solution of U" + U = 0.

A: Given differentiation equation is U''+U=0. We have to find the general solution of the given…

Q: 4. Find the number of non negative solutions to x + y + z = 21. With the conditions that x > 3, y >…

A:

Q: What is the largest number k for which 2x + 3y = 20 and 3x + 4y = k have the same number of positive…

A: Given: 2x+3y=20...............eq(1) 3x+4y=k..................eq(2)   To find:What is the largest…

Q: 3. Verify that 3e-2x +4e* is a solution of y"- 3y' + 2y = 0.

A: We have to verify that 3e-2x+4ex is a solution of y'''-3y'+2y=0

Q: Find the optimal solution. MAX Z=6X+7Y st 4X+5Y≤20 10X+7Y≤35 3X+4Y≥6 X ≥0 , Y ≥0 and an…

A:

Q: 1. Determine all possible solutions of ²u ex² = d²u oy ² by using variable separable method. 7

A: The given problem is to solve the given partial differential equation by using the method of…

Q: prove using the IVT. 2x + 3x = 4x has a solution.

A:

Q: Solve the IVP: X' = AX, where --() 3 1 0 2 -1 0 0 A = 3 and X(0) = -1 2

A:

Q: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

A:

Q: dr a) de rcose + rsene subject to r(0) = 1 (solve by separation of variables)

A:

Q: Find the general solution of the fifth-order DEQ. 2x(5) – 7x(4) + 12x" + 8x" = 0

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Q: 3. Verify that 3e 2x + 4e* is a solution of the y"-3y'+2y=0.

A: We have to verify if the given is a solution to given differential equation or not.

Q: Find the general solution of ylty = 2xcosx -cosX %3D

A:

Q: Show that the equation 2³ + 3y3 = 923 has no solution in integers, other than x = y = z = 0.

A: Suppose that, x3+3y3=9z2 has a non-trivial solution, that is other than (0,0,0), and minimal.

Q: (7) Find the general solution to y = (x +y + 1)

A: Given differential equation is: dydx=x+y+1 Let us assume x+y=t 1+dydx=dtdxdydx=dtdx-1…

Q: In v3 2e" Ve2a + 1

A: I =∫0ln32 exe2x+1 dxTrigonometric substitution;ex = tan uex dx = sec2u duu = tan-1(ex)x = 0 → u =…

Q: Use Gauss Jorden method to solve and also verify the solution. 5x-2y+z=2 3x+2y+7z=3 x+y+3z=2

A:

Q: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

A: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

Q: The equation X2 - 19Y² = 13 has an integral solution, i.e., there is a pair hat x2 19y2= 13. (proof…

A: We have to solve given problems:

Q: 4. a. Prove that 8s + 13 L-1 (s² + 4s – 5) 5(7et +9e-5t) by using completing the square method.

A: Since there are two questions posted, we will answer the first question 4.a). If you want the…

Q: (*") = (") + G) + 5. Prove + 2n2. %3D

A:

Q: Prove that there is a solution of the equation 2° + x² + 4 = 0, x in R.

A:

Q: Verify that y = c1x+c2Vx+ is the general solution of the 6x following nonhomogeneous 2.²y" – xy' + y…

A: Derivative of xn: Derivative of an exponential function that is, xn is given by the formula,…

Q: 3. Find the complete solution of the giyen DE using the Method of Variation of Parameters: y" + 44…

A:

Q: Prove that the equation Z = 1 has no ++ solutions in positive integers x » Y, Z.

A: Assume some value and substitute it many times taking different domains like integers, whole numbers…

Q: Verify that y = ODE y" + 3y' + 2y = 4x². -4e-x-2e-2x + 2x² - 6x +7 is a solution of the SHOW ALL…

A: We have to verify that y=-4e-x-2e-2x+2x2-6x+7 is a solution of the ordinary differential equation…

Q: Function as, y (x) = (x² – 2) (3x + 2) %3D

A: Given,          yx=x2-23x+2

Q: Prove that equation x^2 + y^3 = 60 does not have any positive integer solution. Prove by…

A:

Q: Prove Formulas (1) - (9) Differentiate y = √3x². - 1 √5x = = (3x²)¹/³ – (5x)−¹/2

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.