(9y^2-t^2)/(y^5)(dy)/(dt)+t/(2y^4)=0

解

\frac{9 y ^{2} - t ^{2}}{y ^{5}} \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

y = \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}, y = - - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}

解答ステップ

\frac{9 y ^{2} - t ^{2}}{y ^{5}} \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

完全 ODE を解く:

y = \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}, y = - - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}

y = \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{- 9 + 2 c _{1} t ^{2} + 81}{2 c _{1}}, y = - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}, y = - - \frac{2 c _{1} t ^{2} + 81 + 9}{2 c _{1}}