2xydx=(2-x^2)dy,y(4)=3

Lösung

2 x y d x = (2 - x^{2}) d y, y (4) = 3

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

(1 + y) d y - x d x = 0

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

y^{^{'}} = (y + 2)^{2}

\frac{d y}{d x} = 12 x y - 2 x

y^{^{'}} = (\frac{x}{y}) (\frac{y ^{2} + 1}{x ^{2} - 1})