8y^2(xdy+ydx)=ydx-xdy

Lösung

8 y^{2} (x d y + y d x) = y d x - x d y

y = \frac{c _{1} + c _{1}^{2} + 32 x ^{2}}{16 x}, y = \frac{c _{1} - c _{1}^{2} + 32 x ^{2}}{16 x}

Schritte zur Lösung

8 y^{2} (x d y + y d x) = y d x - x d y

Solve linear ODE:

y = \frac{c _{1} + c _{1}^{2} + 32 x ^{2}}{16 x}, y = \frac{c _{1} - c _{1}^{2} + 32 x ^{2}}{16 x}

y = \frac{c _{1} + c _{1}^{2} + 32 x ^{2}}{16 x}, y = \frac{c _{1} - c _{1}^{2} + 32 x ^{2}}{16 x}

y^{^{'}} = x y - x y^{2}

d r = b (cos (θ) d r + r sin (θ) d θ)

y^{^{'}} = - (x y)^{2}

y^{^{'}} sin (2 x) = y cos (2 x)

y^{2} (x d y - y d x) = 3 x^{2} (y d x - x d y)