ysqrt(1-x^2)*y^'+sqrt(1-y^2)=0

解答

y 1 - x^{2} \cdot y^{^{'}} + 1 - y^{2} = 0

y = - arcsin^{2} (x) + 2 c_{1} arcsin (x) - c_{1}^{2} + 1, y = - - arcsin^{2} (x) + 2 c_{1} arcsin (x) - c_{1}^{2} + 1

求解步骤

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

求解可分离方程:

y = - arcsin^{2} (x) + 2 c_{1} arcsin (x) - c_{1}^{2} + 1, y = - - arcsin^{2} (x) + 2 c_{1} arcsin (x) - c_{1}^{2} + 1

y = - arcsin^{2} (x) + 2 c_{1} arcsin (x) - c_{1}^{2} + 1, y = - - arcsin^{2} (x) + 2 c_{1} arcsin (x) - c_{1}^{2} + 1

y^{^{'}} = \frac{sin ( 2 x )}{cos ( 3 y )}

\frac{d y}{d x} = k (10000 y - y^{2})

(x - 2) d y - (2 y + 3) d x = 0

y^{^{'}} csc (t) = \frac{- y ^{7}}{6}

y^{^{'}} = \frac{ln ( x )}{x y ^{2}}