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

The solution for (d^2y)/(dx^2)-4(dy)/(dx)+3=e^{-5x} is y=c_{1}e^{4x}+c_{2}+1/45 e^{-5x}+(3x)/4

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

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

y = c_{1} e^{4 x} + c_{2} + \frac{1}{45} e^{- 5 x} + \frac{3 x}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} + \frac{1}{45} e^{- 5 x} + \frac{3 x}{4}

y = c_{1} e^{4 x} + c_{2} + \frac{1}{45} e^{- 5 x} + \frac{3 x}{4}

What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)+3=e^{-5x} ?
The solution for (d^2y)/(dx^2)-4(dy)/(dx)+3=e^{-5x} is y=c_{1}e^{4x}+c_{2}+1/45 e^{-5x}+(3x)/4