(x-1)((dy)/(dx))=(4-y^2)

Lösung

(x - 1) (\frac{d y}{d x}) = (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) (\frac{d y}{d 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}

3 x y^{^{'}} - 2 y = 0, y (0) = x^{\frac{2}{3}}

cot (x) (e - y + 1) d x = (1 + sin^{2} (x)) d y

y^{^{'}} arctan (x) - y (1 + x^{2})^{- 1} = 0

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

y^{^{'}} = 14 y + 1