What is the solution for y^{''}+2y=ex+x^3 ?

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

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y^{''}+2y=ex+x^3

y^{^{''}} + 2 y = e x + x^{3}

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

Solution steps

y^{''} (x) + 2 y = e x + x^{3}

Solve linear ODE:

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

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

x \to 9 + lim (\frac{1}{x - 9})

t an g e n t y = x^{4}, (- 1, 1)

d er i v a t i v e 5 t + 6 t^{5}

x \to 2 - lim (x 4 - x^{2})

\frac{d}{d x} (8 x e^{6 x})

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