y^'=5y^{1/5}

Lösung

y^{^{'}} = 5 y^{\frac{1}{5}}

y = \frac{2 \cdot 4 4 3125 t ^{5} + 3125 c _{1} t ^{4} + 1250 c _{1}^{2} t ^{3} + 250 c _{1}^{3} t ^{2} + 25 c _{1}^{4} t + c _{1}^{5}}{5 4 5}, y = - \frac{2 \cdot 4 4 3125 t ^{5} + 3125 c _{1} t ^{4} + 1250 c _{1}^{2} t ^{3} + 250 c _{1}^{3} t ^{2} + 25 c _{1}^{4} t + c _{1}^{5}}{5 4 5}

Schritte zur Lösung

y^{'} (t) = 5 y^{\frac{1}{5}}

Solve separable ODE:

y = \frac{2 \cdot 4 4 3125 t ^{5} + 3125 c _{1} t ^{4} + 1250 c _{1}^{2} t ^{3} + 250 c _{1}^{3} t ^{2} + 25 c _{1}^{4} t + c _{1}^{5}}{5 4 5}, y = - \frac{2 \cdot 4 4 3125 t ^{5} + 3125 c _{1} t ^{4} + 1250 c _{1}^{2} t ^{3} + 250 c _{1}^{3} t ^{2} + 25 c _{1}^{4} t + c _{1}^{5}}{5 4 5}

y = \frac{2 \cdot 4 4 3125 t ^{5} + 3125 c _{1} t ^{4} + 1250 c _{1}^{2} t ^{3} + 250 c _{1}^{3} t ^{2} + 25 c _{1}^{4} t + c _{1}^{5}}{5 4 5}, y = - \frac{2 \cdot 4 4 3125 t ^{5} + 3125 c _{1} t ^{4} + 1250 c _{1}^{2} t ^{3} + 250 c _{1}^{3} t ^{2} + 25 c _{1}^{4} t + c _{1}^{5}}{5 4 5}

\frac{d}{d x} (3 x + \frac{6}{x})

\frac{d}{d x} (\frac{1}{2} sin (x))

\int (e^{x} - 3)^{4} e^{x} d x

\int_{2}^{3} 3 x 2 x^{2} - 1 d x

x \to 0 lim ((2 x + 1) (x - 3))