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

解

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

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

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

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