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

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

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x(dy)/(dx)+(3x+1)y=e^{-3x}

x \frac{d y}{d x} + (3 x + 1) y = e^{- 3 x}

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

Solution steps

x \frac{d y}{d x} + (3 x + 1) y = e^{- 3 x}

Solve linear ODE:

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

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

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x y^{^{'''}} - \frac{2}{x} y^{^{'}} = 0

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