(dy)/(dx)=3(y^5)/(x^4)

解

\frac{d y}{d x} = 3 \frac{y ^{5}}{x ^{4}}

y = 4 - \frac{x ^{3}}{4 ( - 1 + c _{1} x ^{3} )}, y = - 4 - \frac{x ^{3}}{4 ( - 1 + c _{1} x ^{3} )}

解答ステップ

\frac{d y}{d x} = 3 \frac{y ^{5}}{x ^{4}}

分離可能 ODE を解く:

y = 4 - \frac{x ^{3}}{4 ( - 1 + c _{1} x ^{3} )}, y = - 4 - \frac{x ^{3}}{4 ( - 1 + c _{1} x ^{3} )}

y = 4 - \frac{x ^{3}}{4 ( - 1 + c _{1} x ^{3} )}, y = - 4 - \frac{x ^{3}}{4 ( - 1 + c _{1} x ^{3} )}