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

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

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y/x dy=(1+y^2)dx

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

y = e^{x^{2} + c_{1}} - 1, y = - e^{x^{2} + c_{1}} - 1

Solution steps

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

Solve separable ODE:

y = e^{x^{2} + c_{1}} - 1, y = - e^{x^{2} + c_{1}} - 1

y = e^{x^{2} + c_{1}} - 1, y = - e^{x^{2} + c_{1}} - 1

(1 - x^{2}) d y = y d x

\frac{d y}{d x} = - \frac{0.2}{cos ( y )}, y (0) = \frac{π}{4}

y^{^{'}} + 6 y^{3} = 0

\frac{d y}{d x} = 3 x^{2} (y^{2} + 1), y (0) = 1

\frac{d v}{d t} = 0.075 v - 9000

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