(dy)/(dt)=ty^{1/3}

Lösung

\frac{d y}{d t} = t y^{\frac{1}{3}}

y = \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}, y = - \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}

Schritte zur Lösung

\frac{d y}{d t} = t y^{\frac{1}{3}}

Solve separable ODE:

y = \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}, y = - \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}

y = \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}, y = - \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}

d er i v a t i v e 2 + e^{2 t} + e^{- 2 t}

\frac{\partial}{\partial x} (36 (\frac{x}{x + y}) - x)

(x^{2} + 1) (\frac{d y}{d x}) + 8 x (y - 1) = 0, y (0) = 6

\frac{\partial}{\partial x} (2 x^{3} y + 1)

x \to 5 lim (x + 2)