y^'=y^{-1/3}

Lösung

y^{^{'}} = y^{- \frac{1}{3}}

y = \frac{2 2 4 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{4 27}, y = - \frac{2 2 4 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{4 27}

Schritte zur Lösung

y^{'} (t) = y^{- \frac{1}{3}}

Solve separable ODE:

y = \frac{2 2 4 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{4 27}, y = - \frac{2 2 4 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{4 27}

y = \frac{2 2 4 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{4 27}, y = - \frac{2 2 4 t ^{3} + c _{1}^{3} + 3 c _{1} t ^{2} + 3 c _{1}^{2} t}{4 27}

\frac{d y}{d x} = \frac{5 e ^{x}}{e ^{y}}

y^{^{'}} = \frac{x}{y + 1}, y (2) = - 2

\frac{d y}{d t} = \frac{t}{t ^{2} y + y}, y (0) = 8

4 y^{^{'}} + 16 y = 8

3 y^{^{'}} + 2 y = 1 2^{2}