(x/(x^2+y^2))dx-(y/(x^2+y^2))dy=0

Lösung

(\frac{x}{x ^{2} + y ^{2}}) d x - (\frac{y}{x ^{2} + y ^{2}}) d y = 0

y = x^{2} + c_{1}, y = - x^{2} + c_{1}

Schritte zur Lösung

(\frac{x}{x ^{2} + y ^{2}}) d x - (\frac{y}{x ^{2} + y ^{2}}) d y = 0

Solve separable ODE:

y = x^{2} + c_{1}, y = - x^{2} + c_{1}

y = x^{2} + c_{1}, y = - x^{2} + c_{1}

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

x y \cdot y^{^{'}} = y - 1

x e^{x^{2}} + y y^{^{'}} = 0, y (0) = 1

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

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