What is the solution for xy^'=2x^3e^{3x}+2y ?

The solution for xy^'=2x^3e^{3x}+2y is y= 2/3 e^{3x}x^2+c_{1}x^2

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xy^'=2x^3e^{3x}+2y

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

y = \frac{2}{3} e^{3 x} x^{2} + c_{1} x^{2}

Solution steps

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

Solve linear ODE:

y = \frac{2}{3} e^{3 x} x^{2} + c_{1} x^{2}

y = \frac{2}{3} e^{3 x} x^{2} + c_{1} x^{2}

\int \frac{( x - 8 )}{x ^{2} - 7 x + 10} d x

y^{^{''}} + 2 y^{^{'}} + y = 2 e^{x}

\frac{\partial}{\partial y} (e^{- 2 x^{2} - y^{2}})

x \to - \infty lim (b x)

\frac{d}{d x} (ln (sec (x) + tan (x)))

What is the solution for xy^'=2x^3e^{3x}+2y ?
The solution for xy^'=2x^3e^{3x}+2y is y= 2/3 e^{3x}x^2+c_{1}x^2