(dy)/(dx)y=12(3x+1)^{2/3}(4x-2)^{5/4}

Lösung

\frac{d y}{d x} y = 12 (3 x + 1)^{\frac{2}{3}} (4 x - 2)^{\frac{5}{4}}

y = 2 \cdot \int 12 (3 x + 1)^{\frac{2}{3}} (4 x - 2)^{\frac{5}{4}} d x, y = - 2 \cdot \int 12 (3 x + 1)^{\frac{2}{3}} (4 x - 2)^{\frac{5}{4}} d x

Schritte zur Lösung

\frac{d y}{d x} y = 12 (3 x + 1)^{\frac{2}{3}} (4 x - 2)^{\frac{5}{4}}

Solve separable ODE:

y = 2 \cdot \int 12 (3 x + 1)^{\frac{2}{3}} (4 x - 2)^{\frac{5}{4}} d x, y = - 2 \cdot \int 12 (3 x + 1)^{\frac{2}{3}} (4 x - 2)^{\frac{5}{4}} d x

y = 2 \cdot \int 12 (3 x + 1)^{\frac{2}{3}} (4 x - 2)^{\frac{5}{4}} d x, y = - 2 \cdot \int 12 (3 x + 1)^{\frac{2}{3}} (4 x - 2)^{\frac{5}{4}} d x

y^{^{'}} = 1 - 4 y

\frac{d v}{d x} = - 0.002 v - 11

\frac{d y}{d x} = (3 x^{2} y), y (1) = 1

\frac{1}{y} \frac{d y}{d x} = x^{2} + 9

\frac{d y}{d x} (y) = (csc (x) + cot (x))^{- 1}