y(4-x^2)dy=(4+y^2)dx

Lösung

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

y = e^{\frac{1}{2} (l n (\frac{x}{2} + 1) - l n (\frac{x}{2} - 1)) + c_{1}} - 4, y = - e^{\frac{1}{2} (l n (\frac{x}{2} + 1) - l n (\frac{x}{2} - 1)) + c_{1}} - 4

Schritte zur Lösung

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

Solve separable ODE:

y = e^{\frac{1}{2} (l n (\frac{x}{2} + 1) - l n (\frac{x}{2} - 1)) + c_{1}} - 4, y = - e^{\frac{1}{2} (l n (\frac{x}{2} + 1) - l n (\frac{x}{2} - 1)) + c_{1}} - 4

y = e^{\frac{1}{2} (l n (\frac{x}{2} + 1) - l n (\frac{x}{2} - 1)) + c_{1}} - 4, y = - e^{\frac{1}{2} (l n (\frac{x}{2} + 1) - l n (\frac{x}{2} - 1)) + c_{1}} - 4

\frac{d y}{d x} + 2 x y = 25 x

x y^{^{'}} + 4 y + 8 = 0

\frac{d y}{d x} = - 3 x^{2} y

\frac{d y}{d x} y = x e^{- 4 x}

y^{^{'}} = \frac{2 e ^{4 y}}{x ^{4}}