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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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