What is the solution for xsqrt(1+y^2)dx-dy=0 ?

The solution for xsqrt(1+y^2)dx-dy=0 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=0

x 1 + y^{2} d x - d y = 0

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 = 0

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 y}{y} = \frac{d x}{( x - 9 ) ^{2} - 5 ^{2}}

y^{^{'}} = - \frac{0.1 y}{0.5 - 0.025 x}

4 y^{11} + y^{^{'}} = 0

\frac{d p}{d t} = t^{2} p - 7 p + t^{2} - 7

6 \frac{d y}{d x} + 5 x^{2} y = 97 x^{2}

What is the solution for xsqrt(1+y^2)dx-dy=0 ?
The solution for xsqrt(1+y^2)dx-dy=0 is y=-1/(2e^{(x^2+2c_{1))/2}}+(e^{(x^2+2c_{1})/2})/(2)