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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

y^{^{'}} + 21 \frac{y}{x} = 0

\frac{d x}{d y} = sec (x)

2 y^{^{'}} + 2 y = 10, y (0) = 0

2 x y d x = (5 - x^{2}) d y

y^{^{'}} = y^{2} + 1, y (1) = 0