What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)-3y=24e^{3x} ?

The solution for (d^2y)/(dx^2)+2(dy)/(dx)-3y=24e^{3x} is y=c_{1}e^x+c_{2}e^{-3x}+2e^{3x}

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(d^2y)/(dx^2)+2(dy)/(dx)-3y=24e^{3x}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 3 y = 24 e^{3 x}

y = c_{1} e^{x} + c_{2} e^{- 3 x} + 2 e^{3 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 3 y = 24 e^{3 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} + 2 e^{3 x}

y = c_{1} e^{x} + c_{2} e^{- 3 x} + 2 e^{3 x}

y^{^{''}} - y^{^{'}} - 2 y = 8 sin (t) - 2 cos (t)

y^{^{''}} + 6 y^{^{'}} + 13 y = 13 x^{2}

2 y^{^{''}} - y^{^{'}} - y = t + 1, y (0) = 1, y^{^{'}} (0) = 0

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

x^{^{''}} - 6 x^{^{'}} + 9 x = 2 t e^{3 t}

What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)-3y=24e^{3x} ?
The solution for (d^2y)/(dx^2)+2(dy)/(dx)-3y=24e^{3x} is y=c_{1}e^x+c_{2}e^{-3x}+2e^{3x}