What is the solution for y^{''}+y=e^x+x^3 ?

The solution for y^{''}+y=e^x+x^3 is y=c_{1}cos(x)+c_{2}sin(x)+1/2 e^x+x^3-6x

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y^{''}+y=e^x+x^3

y^{^{''}} + y = e^{x} + x^{3}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{2} e^{x} + x^{3} - 6 x

Solution steps

y^{''} (x) + y = e^{x} + x^{3}

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{2} e^{x} + x^{3} - 6 x

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{2} e^{x} + x^{3} - 6 x

y^{^{''}} + y = 1 + 2 t sin (t)

y^{^{''}} + 16 y = sec (4)

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

0.25 y^{^{''}} + y^{^{'}} + y = x^{2} - 2 x

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + y = x

What is the solution for y^{''}+y=e^x+x^3 ?
The solution for y^{''}+y=e^x+x^3 is y=c_{1}cos(x)+c_{2}sin(x)+1/2 e^x+x^3-6x