What is the solution for (dy)/(dx)+4y-e^{-x}=0 ?

The solution for (dy)/(dx)+4y-e^{-x}=0 is y= 1/(3e^x)+(c_{1})/(e^{4x)}

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(dy)/(dx)+4y-e^{-x}=0

\frac{d y}{d x} + 4 y - e^{- x} = 0

y = \frac{1}{3 e ^{x}} + \frac{c _{1}}{e ^{4 x}}

Solution steps

\frac{d y}{d x} + 4 y - e^{- x} = 0

Solve linear ODE:

y = \frac{1}{3 e ^{x}} + \frac{c _{1}}{e ^{4 x}}

y = \frac{1}{3 e ^{x}} + \frac{c _{1}}{e ^{4 x}}

\frac{e ^{- s}}{s ^{2} + 2 s + 2}

0

y^{^{'}} = ry (s - y)

\frac{d}{d x} (3^{x^{2}} + 2)

\int e^{- 6 x} sin (3 x) d x

What is the solution for (dy)/(dx)+4y-e^{-x}=0 ?
The solution for (dy)/(dx)+4y-e^{-x}=0 is y= 1/(3e^x)+(c_{1})/(e^{4x)}