What is the solution for (d^2y)/(dx^2)+9y=-15x+7+e^x ?

The solution for (d^2y)/(dx^2)+9y=-15x+7+e^x is y=c_{1}cos(3x)+c_{2}sin(3x)-(5x)/3+7/9+1/10 e^x

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(d^2y)/(dx^2)+9y=-15x+7+e^x

\frac{d ^{2} y}{d x ^{2}} + 9 y = - 15 x + 7 + e^{x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{5 x}{3} + \frac{7}{9} + \frac{1}{10} e^{x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 9 y = - 15 x + 7 + e^{x}

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{5 x}{3} + \frac{7}{9} + \frac{1}{10} e^{x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{5 x}{3} + \frac{7}{9} + \frac{1}{10} e^{x}

y^{^{''}} + 9 y = sin (3 x) + e^{2 x}

y^{^{''}} - y^{^{'}} - 2 y = 8 x + 5

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 e^{3 t}

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

y^{^{''}} - 8 y^{^{'}} - 4 y - 2 = 10 x^{2} - 2 x e^{2}

What is the solution for (d^2y)/(dx^2)+9y=-15x+7+e^x ?
The solution for (d^2y)/(dx^2)+9y=-15x+7+e^x is y=c_{1}cos(3x)+c_{2}sin(3x)-(5x)/3+7/9+1/10 e^x