What is the solution for (d^2y)/(dx^2)+(dy)/(dx)-6y=4e^{-x} ?

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

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(d^2y)/(dx^2)+(dy)/(dx)-6y=4e^{-x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 4 e^{- x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 4 e^{- x}

Solve linear ODE:

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

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

cos^{2} (2 x)

\int \frac{x ^{5}}{x ^{3} - 8} d x

f (x) = - 4.9 x^{2} + 35 x + 4

\frac{x}{x - 2}

\frac{d}{d x} (x^{2} e^{x y})

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