(x-1)y^'=4-y^2

Lösung

(x - 1) y^{^{'}} = 4 - y^{2}

y = - \frac{2 e ^{4 c_{1}} x ^{4}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x ^{3}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{12 e ^{4 c_{1}} x ^{2}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2 e ^{4 c_{1}}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x}

Schritte zur Lösung

(x - 1) y^{'} (x) = 4 - y^{2}

Solve separable ODE:

y = - \frac{2 e ^{4 c_{1}} x ^{4}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x ^{3}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{12 e ^{4 c_{1}} x ^{2}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2 e ^{4 c_{1}}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x}

y = - \frac{2 e ^{4 c_{1}} x ^{4}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x ^{3}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{12 e ^{4 c_{1}} x ^{2}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2 e ^{4 c_{1}}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x}

y^{^{'}} + y = 2 y^{\frac{1}{2}}

\frac{d}{d θ} (r (θ)) + r (θ) tan (θ) = 3 tan (θ)

(x + 1) \frac{d y}{d x} = 2 y

\frac{d v}{d t} = - 0.4 \cdot v

\frac{d y}{d t} = \frac{2 t}{y + y t ^{2}}