What is the solution for y^{''}+9y=5e^x-162x^2 ?

The solution for y^{''}+9y=5e^x-162x^2 is y=c_{1}cos(3x)+c_{2}sin(3x)+1/2 e^x-18x^2+4

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y^{''}+9y=5e^x-162x^2

y^{^{''}} + 9 y = 5 e^{x} - 162 x^{2}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{2} e^{x} - 18 x^{2} + 4

Solution steps

y^{''} (x) + 9 y = 5 e^{x} - 162 x^{2}

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{2} e^{x} - 18 x^{2} + 4

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{2} e^{x} - 18 x^{2} + 4

What is the solution for y^{''}+9y=5e^x-162x^2 ?
The solution for y^{''}+9y=5e^x-162x^2 is y=c_{1}cos(3x)+c_{2}sin(3x)+1/2 e^x-18x^2+4