What is the solution for y*ln(x)-x^2y=xy^' ?

The solution for y*ln(x)-x^2y=xy^' is y=e^{c_{1}+(-x^2+ln^2(x))/2}

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y*ln(x)-x^2y=xy^'

y \cdot ln (x) - x^{2} y = x y^{^{'}}

y = e^{c_{1} + \frac{- x ^{2} + l n ^{2} ( x )}{2}}

Solution steps

y \cdot ln (x) - x^{2} y = x y^{'} (x)

Solve separable ODE:

y = e^{c_{1} + \frac{- x ^{2} + l n ^{2} ( x )}{2}}

y = e^{c_{1} + \frac{- x ^{2} + l n ^{2} ( x )}{2}}

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6 e^{- 5 t} \cdot cos (t)

What is the solution for y*ln(x)-x^2y=xy^' ?
The solution for y*ln(x)-x^2y=xy^' is y=e^{c_{1}+(-x^2+ln^2(x))/2}