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

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

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(dy)/(dx)+6y=xe^{-6x}

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

y = \frac{x ^{2}}{2 e ^{6 x}} + \frac{c _{1}}{e ^{6 x}}

Solution steps

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

Solve linear ODE:

y = \frac{x ^{2}}{2 e ^{6 x}} + \frac{c _{1}}{e ^{6 x}}

y = \frac{x ^{2}}{2 e ^{6 x}} + \frac{c _{1}}{e ^{6 x}}

\frac{\partial}{\partial x} (48 x^{7} y^{7} + 30 x^{5} y^{5})

\frac{d}{d x} (- 3 7 x - 1)

\int o d o

f (t) = 1 + ln (t)

2 y y^{^{'}} + 2 = y^{2} + 2 x, y (0) = 8

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