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

解

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

y = \frac{x ^{4} + 4 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}, y = - \frac{x ^{4} + 4 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}

解答ステップ

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

分離可能 ODE を解く:

y = \frac{x ^{4} + 4 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}, y = - \frac{x ^{4} + 4 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}

y = \frac{x ^{4} + 4 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}, y = - \frac{x ^{4} + 4 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}