(ydy)/(xdx)=(sqrt(y^2+1))/(sqrt(x^2+1))

解

\frac{y d y}{x d x} = \frac{y ^{2} + 1}{x ^{2} + 1}

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

解答ステップ

\frac{y d y}{x d x} = \frac{y ^{2} + 1}{x ^{2} + 1}

分離可能 ODE を解く:

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

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