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

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

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

\frac{x 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

\frac{x 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}

\int \frac{8 x}{( 2 x ^{2} + 5 ) ^{4}} d x

x \to 0 lim (\frac{sin ( 5 x )}{tan ( 6 x )})

\int \frac{1}{x ( 4 - ln ^{2} ( x ) )} d x

f (x) = \frac{- 9 x}{2 x - 1}

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