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

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

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xsqrt(1+y^2)dx=dy

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

y = - \frac{1}{2 e ^{\frac{x ^{2} + 2 c _{1}}{2}}} + \frac{e ^{\frac{x ^{2} + 2 c _{1}}{2}}}{2}

Solution steps

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

Solve separable ODE:

y = - \frac{1}{2 e ^{\frac{x ^{2} + 2 c _{1}}{2}}} + \frac{e ^{\frac{x ^{2} + 2 c _{1}}{2}}}{2}

y = - \frac{1}{2 e ^{\frac{x ^{2} + 2 c _{1}}{2}}} + \frac{e ^{\frac{x ^{2} + 2 c _{1}}{2}}}{2}

\frac{d}{d x} (\frac{ln ( x )}{5 x ^{3}})

\int 7 x sec^{2} (x) d x

10000 - 9000 e^{- 0.3 t}

\frac{s}{( s - 1 ) ^{2}}

y = 2 x^{\frac{3}{2}}

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