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

Lösung

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

y = - \frac{2}{arcsin ^{2} ( x ) + 2 c _{1}} + \frac{arcsin ^{2} ( x )}{arcsin ^{2} ( x ) + 2 c _{1}} + \frac{2 c _{1}}{arcsin ^{2} ( x ) + 2 c _{1}}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{2}{arcsin ^{2} ( x ) + 2 c _{1}} + \frac{arcsin ^{2} ( x )}{arcsin ^{2} ( x ) + 2 c _{1}} + \frac{2 c _{1}}{arcsin ^{2} ( x ) + 2 c _{1}}

y = - \frac{2}{arcsin ^{2} ( x ) + 2 c _{1}} + \frac{arcsin ^{2} ( x )}{arcsin ^{2} ( x ) + 2 c _{1}} + \frac{2 c _{1}}{arcsin ^{2} ( x ) + 2 c _{1}}

\frac{d y}{d x} = 8 x y

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

\frac{d y}{d x} = (y x^{2})

\frac{d x}{x ^{2} y} + \frac{d y}{x y ^{2}} = 0

y^{^{'}} + \frac{y}{3} = 4, y (- 1) = 0