What is the solution for y^'=(13x)/(y+x^2y) ?

The solution for y^'=(13x)/(y+x^2y) is y=sqrt(13ln(1+x^2)+c_{1)},y=-sqrt(13ln(1+x^2)+c_{1)}

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y^'=(13x)/(y+x^2y)

y^{^{'}} = \frac{13 x}{y + x ^{2} y}

y = 13 ln (1 + x^{2}) + c_{1}, y = - 13 ln (1 + x^{2}) + c_{1}

Solution steps

y^{'} (x) = \frac{13 x}{y + x ^{2} y}

Solve separable ODE:

y = 13 ln (1 + x^{2}) + c_{1}, y = - 13 ln (1 + x^{2}) + c_{1}

y = 13 ln (1 + x^{2}) + c_{1}, y = - 13 ln (1 + x^{2}) + c_{1}

x^{^{'}} = x + x a^{2}

x 1 + y^{2} + x y^{^{'}} 1 + x^{2} = 0

\frac{d y}{d x} = 5 x^{2} y^{3}

\frac{d y}{d x} (x^{2} + 2) + 4 x (y^{2} + 2 y + 1) = 0

x \cdot \frac{d y}{d x} = 3 y

What is the solution for y^'=(13x)/(y+x^2y) ?
The solution for y^'=(13x)/(y+x^2y) is y=sqrt(13ln(1+x^2)+c_{1)},y=-sqrt(13ln(1+x^2)+c_{1)}