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

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

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

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

y = 2 x + \frac{2 x ^{3}}{3} + c_{1}, y = - 2 x + \frac{2 x ^{3}}{3} + c_{1}

Solution steps

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

Solve separable ODE:

y = 2 x + \frac{2 x ^{3}}{3} + c_{1}, y = - 2 x + \frac{2 x ^{3}}{3} + c_{1}

y = 2 x + \frac{2 x ^{3}}{3} + c_{1}, y = - 2 x + \frac{2 x ^{3}}{3} + c_{1}

(8 + x) \frac{d y}{d x} = 5 y

\frac{d y}{d x} + 7 x y = 8 x, y (0) = 6

\frac{d y}{d x} + 7 x y = 8 x, y (0) = 5

y^{^{'}} = y x e^{x}

\frac{d V}{d t} = 90 - \frac{7 V}{100}, V (0) = 0

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