(dy)/(dt)=y^{1/3}t^{2/5}

Lösung

\frac{d y}{d t} = y^{\frac{1}{3}} t^{\frac{2}{5}}

y = \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}, y = - \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}

Schritte zur Lösung

\frac{d y}{d t} = y^{\frac{1}{3}} t^{\frac{2}{5}}

Solve separable ODE:

y = \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}, y = - \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}

y = \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}, y = - \frac{2 2 125 t ^{\frac{21}{5}} + 525 c _{1} t ^{\frac{14}{5}} + 735 c _{1}^{2} t ^{\frac{7}{5}} + 343 c _{1}^{3}}{21 21}

d er i v a t i v e 38 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

s l o p e y = \frac{1}{1 - x}, x = 3

\frac{d y}{d x} = 6 y (10 - y)

\int \frac{1 + x + x}{x} d x

d er i v a t i v e \frac{x ^{2}}{x + 1}