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

Lösung

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}

Schritte zur Lösung

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}}

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

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

\frac{d y}{d t} = y \cdot t^{3} - 1.5 \cdot y

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