What is the solution for y^{''}-y=2x^4+5x^2-10x ?

The solution for y^{''}-y=2x^4+5x^2-10x is y=c_{1}e^x+c_{2}e^{-x}-2x^4-29x^2+10x-58

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y^{''}-y=2x^4+5x^2-10x

y^{^{''}} - y = 2 x^{4} + 5 x^{2} - 10 x

y = c_{1} e^{x} + c_{2} e^{- x} - 2 x^{4} - 29 x^{2} + 10 x - 58

Solution steps

y^{''} (x) - y = 2 x^{4} + 5 x^{2} - 10 x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - 2 x^{4} - 29 x^{2} + 10 x - 58

y = c_{1} e^{x} + c_{2} e^{- x} - 2 x^{4} - 29 x^{2} + 10 x - 58

y^{^{''}} + 2 y^{^{'}} + 5 y = 4 e^{(- x)} - x cos (2 x)

(D^{2} + 1) y = sin (x) sin (2 x)

y^{^{''}} + 16 y = sin (3 x)

2 x^{^{''}} - x^{^{'}} + 3 t = 5

y^{^{''}} - 2 y^{^{'}} + 82 y = e x cos (9 x)

What is the solution for y^{''}-y=2x^4+5x^2-10x ?
The solution for y^{''}-y=2x^4+5x^2-10x is y=c_{1}e^x+c_{2}e^{-x}-2x^4-29x^2+10x-58