What is the solution for (d^2y)/(dx^2)+5(dy)/(dx)+6y=12e^x ?

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

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(d^2y)/(dx^2)+5(dy)/(dx)+6y=12e^x

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = 12 e^{x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = 12 e^{x}

Solve linear ODE:

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

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

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