-(D² – 25) y = x e* . Using method of undetermined coefficients, what is y Consider A ' = Ax e* + B e*

Q: 1. Let y = x2 + x +4+ Find y'.

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Q: x3 1+x² dx

A: Note : according to our guidelines I can solve only one question, please reroute the remaining one.

Q: 8. y" – y = 5sin²(x); when y(0) = 2, y'(0) = -4 %D

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Q: What is the coefficient of x2y' in (5x- y)?

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Q: Is the function y = Cx? a solution to the ODE y" – xy' + y = 0?

A: Using Derivatives.

Q: Find the 2nd solution using reduction of order. t²y" - 4ty +6y=0;t> 0; y₁=t²

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Q: Solve by reduction of order. Find y2 and y (x² + 1)y" – 2xy' + 2y = 0 yı = x -

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Q: Use variation of parameters to find a particular solution of y" - y =

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Q: y" – 2y' + y = -3 –x+x, y(0) = -2, y(0) = 1.

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Q: 8.) y" +2y' +5y = 3e 2* ; and y(0) = y'(0) = 1

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Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

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Q: (e) y(ª) – 4y "= 5x² -e2* (g) y(“) +8y '= 4

A: The given differential equation is y(4)-4y''=5x2-e2x

Q: (C) y" + 21y+8x=y" + 5y' + e²*

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Q: Let y1, Y2 be two independent solutions of (t 1)y"- ty' +y = 0. If W(y1, Y2)(2) = e2, then W(y1,…

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Q: What is the solution of the given ODE xy' + y = Vx

A: Given: xy'+y=x

Q: y(4) - 4y" + 6y" - 4y+y=0; y(0) = 0, y'(0) = 1, y'(0) = 0, y" (0) = 1

A: The Laplace transform is used to find the solution of the linear ordinary differential equation with…

Q: 8. x(x² + 1)y' + 2y = (x² + 1)³

A: Given problem:- xx2+1y'+2y=x2+13

Q: If r(y) = e³y² +3 find r'(y) =

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Q: If y" – 6y' + 9y = 0, y1 = e3x, y2 = xe3x = 3 and y'(0) = 12 then find c1 and c2 %3! (а) C1 = 5, c2…

A: We have to find constant

Q: y''+4y'–1=0

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Q: 2 calculate J= e dyok 2x

A: Given integral :

Q: Answer: y = -(e-x + c)/(1 + x2)

A: Given differential equation is,

Q: Use the reduction of order method to solve the equation y" + 2y' + y = 2e-

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Q: y (2 xy +1)= xy'

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Q: go- 2- 3y = *2+ 3x}

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Q: (1) y "'+ y "– 2y = 3+2cosx

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Q: Q2: Solve the ODE =n, x²y" + xy' - y = - x+1

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Q: x²-2x* 5. Integrate with respect to x x4

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