What is the solution for xy^'+(3x+1)y=e^{(-3x)} ?

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

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xy^'+(3x+1)y=e^{(-3x)}

x y^{^{'}} + (3 x + 1) y = e^{(- 3 x)}

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

Solution steps

x y^{'} (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}

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