xyy^'=sqrt(1-y^2)

解

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

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

解答ステップ

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

分離可能 ODE を解く:

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

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