What is the solution for (d^2y)/(dx^2)+y=2e^{3x} ?

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

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(d^2y)/(dx^2)+y=2e^{3x}

\frac{d ^{2} y}{d x ^{2}} + y = 2 e^{3 x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = 2 e^{3 x}

Solve linear ODE:

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

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

y^{^{'''}} - y^{^{''}} - 4 y^{^{'}} + 4 y = 10 e^{3 t}

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

(d^{2} - 4 d + 3) y = e^{3 x} cos (x)

y^{^{''}} - 4 y^{^{'}} + 4 y = 4 t^{2} - 4 t + 26

y^{^{''}} + \frac{y ^{^{'}}}{2} - \frac{y}{2} = \frac{x + 1}{2}

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