What is the solution for y'=(e^{3*x}+3*x*y+y)/x ?

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

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y'=(e^{3x}+3x*y+y)/x

y^{^{'}} = \frac{e ^{3 \cdot x} + 3 \cdot x \cdot y + y}{x}

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

Solution steps

y^{'} (x) = \frac{e ^{3 \cdot x} + 3 \cdot x \cdot y + y}{x}

Solve linear ODE:

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

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

\int \frac{1}{2 - 7 x} d x

sin ((π x)^{9})

[x^{2} (x^{2} + 5 x)]^{6}

f (x) = y^{2} - x y

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