What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)-12y=3e^{5x} ?

The solution for (d^2y)/(dx^2)-4(dy)/(dx)-12y=3e^{5x} is y=c_{1}e^{6x}+c_{2}e^{-2x}-3/7 e^{5x}

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(d^2y)/(dx^2)-4(dy)/(dx)-12y=3e^{5x}

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 y = 3 e^{5 x}

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{3}{7} e^{5 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 y = 3 e^{5 x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{3}{7} e^{5 x}

y = c_{1} e^{6 x} + c_{2} e^{- 2 x} - \frac{3}{7} e^{5 x}

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 y = cos (x)

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

\frac{d ^{2} y}{d x ^{2}} - 16 y = 9 e^{4 x} + 30 e^{x}

y^{^{''}} - 5 y^{^{'}} + 6 y^{^{'}} = x^{2}

2 y^{^{''}} + 3 y^{^{'}} + y = lo g_{10} (x)

What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)-12y=3e^{5x} ?
The solution for (d^2y)/(dx^2)-4(dy)/(dx)-12y=3e^{5x} is y=c_{1}e^{6x}+c_{2}e^{-2x}-3/7 e^{5x}