What is the solution for y^{''}-2y^'+5y=25x^2+12 ?

The solution for y^{''}-2y^'+5y=25x^2+12 is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))+5x^2+4x+2

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y^{''}-2y^'+5y=25x^2+12

y^{^{''}} - 2 y^{^{'}} + 5 y = 25 x^{2} + 12

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + 2

Solution steps

y^{''} (x) - 2 y^{'} (x) + 5 y = 25 x^{2} + 12

Solve linear ODE:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + 2

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + 2

What is the solution for y^{''}-2y^'+5y=25x^2+12 ?
The solution for y^{''}-2y^'+5y=25x^2+12 is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))+5x^2+4x+2