What is the solution for y^'+5y=e^{-3x} ?

The solution for y^'+5y=e^{-3x} is y= 1/(2e^{3x)}+(c_{1})/(e^{5x)}

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y^'+5y=e^{-3x}

y^{^{'}} + 5 y = e^{- 3 x}

y = \frac{1}{2 e ^{3 x}} + \frac{c _{1}}{e ^{5 x}}

Solution steps

y^{'} (x) + 5 y = e^{- 3 x}

Solve linear ODE:

y = \frac{1}{2 e ^{3 x}} + \frac{c _{1}}{e ^{5 x}}

y = \frac{1}{2 e ^{3 x}} + \frac{c _{1}}{e ^{5 x}}

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\frac{d y}{d x} = x^{3} + x^{2} - 5 x + 11

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