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

Lösung

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

y = \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}, y = - \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}, y = - \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}

y = \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}, y = - \frac{2 2 x ^{3} + c _{1}^{3} + 3 c _{1} x ^{2} + 3 c _{1}^{2} x}{3 3}

d x + cos (t) x d t - cos (t) d t = 0, x (0) = - 1

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

\frac{d y}{d t} = (y t)^{\frac{1}{5}}

sin (x) \frac{d y}{d x} + (cos (x)) y = 0

y^{^{'}} + 2 \cdot \frac{y}{x} = 0