y^'=3.2y^{2/3}

Lösung

y^{^{'}} = 3.2 y^{\frac{2}{3}}

y = \frac{4096 t ^{3}}{3375} + \frac{256 c _{1} t ^{2}}{225} + \frac{16 c _{1}^{2} t}{45} + \frac{c _{1}^{3}}{27}

Schritte zur Lösung

y^{'} (t) = 3.2 y^{\frac{2}{3}}

Solve separable ODE:

y = \frac{4096 t ^{3}}{3375} + \frac{256 c _{1} t ^{2}}{225} + \frac{16 c _{1}^{2} t}{45} + \frac{c _{1}^{3}}{27}

y = \frac{4096 t ^{3}}{3375} + \frac{256 c _{1} t ^{2}}{225} + \frac{16 c _{1}^{2} t}{45} + \frac{c _{1}^{3}}{27}

y^{^{'}} = k \cdot (y - c)

\frac{d V}{d t} = k (40 - V)

\frac{1}{y} d x - \frac{x}{y ^{2}} d y = 0

y y^{^{'}} = 3 x^{3} - 5

y^{^{'}} = - y^{2}, y (0) = 0.5