What is the solution for (2xy+x^3)y^'= 1/2 x^2y+y^2 ?

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

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(2xy+x^3)y^'= 1/2 x^2y+y^2

(2 x y + x^{3}) y^{^{'}} = \frac{1}{2} x^{2} y + y^{2}

y = c_{1} x

Solution steps

(2 x y + x^{3}) y^{'} (x) = \frac{1}{2} x^{2} y + y^{2}

Solve separable ODE:

y = c_{1} x

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x \to - 4 lim (9 x + 11)

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\frac{\partial}{\partial y} (x^{3} y + e^{x y^{2}})

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n = 0 \sum \infty \frac{( - 1 ) ^{n} 7 ^{n} x ^{n}}{5 ^{n + 1}}

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