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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

(x^{2} - 9) y^{^{'}} + x y = 0

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

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

\frac{d r}{d t} = 0.1872 \cdot r

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

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