What is the solution for y^'=(9x)/(y+x^2y),y(0)=-7 ?

The solution for y^'=(9x)/(y+x^2y),y(0)=-7 is y=-sqrt(9ln(1+x^2)+49)

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y^'=(9x)/(y+x^2y),y(0)=-7

y^{^{'}} = \frac{9 x}{y + x ^{2} y}, y (0) = - 7

y = - 9 ln (1 + x^{2}) + 49

Solution steps

y^{'} (x) = \frac{9 x}{y + x ^{2} y}

Solve separable ODE:

y = - 9 ln (1 + x^{2}) + 49

y = - 9 ln (1 + x^{2}) + 49

\frac{d y}{d x} = - \frac{4}{7} x^{3} y^{3}

\frac{d x}{d y} - \frac{1}{y} = \frac{2 x}{2 y}, y (1) = 2

\frac{d y}{d x} = \frac{- 2 x y}{x ^{2} + 1}

a (x d y + 2 y d x) = x y d x

y^{^{'}} = y x

What is the solution for y^'=(9x)/(y+x^2y),y(0)=-7 ?
The solution for y^'=(9x)/(y+x^2y),y(0)=-7 is y=-sqrt(9ln(1+x^2)+49)