What is the solution for (xdx}{sqrt(1+x^2)}=\frac{dy)/y ?

The solution for (xdx}{sqrt(1+x^2)}=\frac{dy)/y is y=e^{sqrt(x^2+1)+c_{1}}

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(xdx}{sqrt(1+x^2)}=\frac{dy)/y

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} = 2 x y, y (1) = 5

x^{^{'}} = 20 t - \frac{4 x}{30} t

2 x y \frac{d y}{d x} = 6 + 14 ln (x)

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

y d x - x d y = y^{3} + y^{2} x d y

What is the solution for (xdx}{sqrt(1+x^2)}=\frac{dy)/y ?
The solution for (xdx}{sqrt(1+x^2)}=\frac{dy)/y is y=e^{sqrt(x^2+1)+c_{1}}