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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} - \frac{y}{4} = 0

y^{^{'}} - y = 0, y (0) = cosh (3 t), y (0) = 1

\frac{d y}{d x} = 4 x (9 - y^{2})^{\frac{1}{2}}

(10 x - 1) y^{^{'}} + 10 y = 0

y^{^{'}} = e^{2 y - x}, y (0) = - 1

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