What is the solution for y^{''}+1y=xe^{5x} ?

The solution for y^{''}+1y=xe^{5x} is y=c_{1}cos(x)+c_{2}sin(x)+(e^{5x}x)/(26)-5/338 e^{5x}

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y^{''}+1y=xe^{5x}

y^{^{''}} + 1 y = x e^{5 x}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{e ^{5 x} x}{26} - \frac{5}{338} e^{5 x}

Solution steps

y^{''} (x) + 1 y = x e^{5 x}

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{e ^{5 x} x}{26} - \frac{5}{338} e^{5 x}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{e ^{5 x} x}{26} - \frac{5}{338} e^{5 x}

\frac{\partial}{\partial x} (x^{2} sin (x y + z))

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

(x + 2) (x - 5) (x - 1)

x \to 0 lim (3 (h + 2 x) 2)

\int \frac{5}{x + 2} d x

What is the solution for y^{''}+1y=xe^{5x} ?
The solution for y^{''}+1y=xe^{5x} is y=c_{1}cos(x)+c_{2}sin(x)+(e^{5x}x)/(26)-5/338 e^{5x}