(dy)/(dx)=\sqrt[3]{y},y(0)=5.2

Lösung

\frac{d y}{d x} = 3 y, y (0) = 5.2

y = \frac{2 50 \cdot 2 5 ^{\frac{2}{3}} x ^{3} + 225 \cdot 2 ^{\frac{2}{3}} 3 4225 x ^{2} + 675 \cdot 16 9 ^{\frac{2}{3}} 3 2 x + 4563 \cdot 2 5 ^{\frac{2}{3}}}{2 5 ^{\frac{1}{3}} \cdot 15 3}

Schritte zur Lösung

\frac{d y}{d x} = 3 y

Solve separable ODE:

y = \frac{2 50 \cdot 2 5 ^{\frac{2}{3}} x ^{3} + 225 \cdot 2 ^{\frac{2}{3}} 3 4225 x ^{2} + 675 \cdot 16 9 ^{\frac{2}{3}} 3 2 x + 4563 \cdot 2 5 ^{\frac{2}{3}}}{2 5 ^{\frac{1}{3}} \cdot 15 3}

y = \frac{2 50 \cdot 2 5 ^{\frac{2}{3}} x ^{3} + 225 \cdot 2 ^{\frac{2}{3}} 3 4225 x ^{2} + 675 \cdot 16 9 ^{\frac{2}{3}} 3 2 x + 4563 \cdot 2 5 ^{\frac{2}{3}}}{2 5 ^{\frac{1}{3}} \cdot 15 3}

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

a y^{2} + \frac{d y}{d x} = 0

\frac{d y}{d t} + 4 y = 11, y (0) = 1

(1 + y^{2}) d x - (x + x^{2}) d y = 0

\frac{x ^{2}}{1 + x ^{3}} d x - \frac{1}{y} d y = 0