What is the solution for xe^yy^'=2(e^y+x^3e^{2x}) ?

The solution for xe^yy^'=2(e^y+x^3e^{2x}) is y=ln(c_{1}x^2+e^{2x}x^2)

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xe^yy^'=2(e^y+x^3e^{2x})

x e^{y} y^{^{'}} = 2 (e^{y} + x^{3} e^{2 x})

y = ln (c_{1} x^{2} + e^{2 x} x^{2})

Solution steps

x e^{y} y^{'} (x) = 2 (e^{y} + x^{3} e^{2 x})

Solve exact ODE:

y = ln (c_{1} x^{2} + e^{2 x} x^{2})

y = ln (c_{1} x^{2} + e^{2 x} x^{2})

\int 1 + (\frac{1}{x})^{2} d x

x \to 0 lim (3 f (x) (x^{2}))

\int cos (3 x) d x

x \to 0 + lim (x ln (2 x))

\int v^{\frac{1}{2}} d v

What is the solution for xe^yy^'=2(e^y+x^3e^{2x}) ?
The solution for xe^yy^'=2(e^y+x^3e^{2x}) is y=ln(c_{1}x^2+e^{2x}x^2)