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

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

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

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

y = \frac{x ^{2}}{2 e ^{4 x}} + \frac{c _{1}}{e ^{4 x}}

Solution steps

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

Solve linear ODE:

y = \frac{x ^{2}}{2 e ^{4 x}} + \frac{c _{1}}{e ^{4 x}}

y = \frac{x ^{2}}{2 e ^{4 x}} + \frac{c _{1}}{e ^{4 x}}

\frac{d}{d x} (4 - ∣ x ∣)

\int \frac{e ^{3 x}}{( 1 - 2 e ^{3 x} ) ^{2}} d x

\frac{d}{d x} (1 - (1 + x) e^{- x})

\int \frac{1}{( 2 + x ) 1 + x} d x

f (x) = x^{4} - 2 x^{2} + 1, at x = 2

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