y^'=y^{1/3}

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

\frac{d y}{d x} = 5 x + 15 y

f (x) = \frac{x}{4 x + 3 ln ( x )}

s l o p e y = \frac{- 4 x ^{2} + 12}{2 x + 2}

\frac{d}{d x} (arcsin (e^{- x}))

x \to - 9 lim (1 - 4 x^{3})