(dy)/(dx)=((3y+2)/(5x+4))^2

Lösung

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

y = - \frac{25 x}{9 ( - 1 + 25 c _{1} x + 20 c _{1} )} - \frac{50 c _{1} x}{3 ( 25 c _{1} x + 20 c _{1} - 1 )} - \frac{40 c _{1}}{3 ( 25 c _{1} x + 20 c _{1} - 1 )} - \frac{14}{9 ( - 1 + 25 c _{1} x + 20 c _{1} )}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{25 x}{9 ( - 1 + 25 c _{1} x + 20 c _{1} )} - \frac{50 c _{1} x}{3 ( 25 c _{1} x + 20 c _{1} - 1 )} - \frac{40 c _{1}}{3 ( 25 c _{1} x + 20 c _{1} - 1 )} - \frac{14}{9 ( - 1 + 25 c _{1} x + 20 c _{1} )}

y = - \frac{25 x}{9 ( - 1 + 25 c _{1} x + 20 c _{1} )} - \frac{50 c _{1} x}{3 ( 25 c _{1} x + 20 c _{1} - 1 )} - \frac{40 c _{1}}{3 ( 25 c _{1} x + 20 c _{1} - 1 )} - \frac{14}{9 ( - 1 + 25 c _{1} x + 20 c _{1} )}

\int ln (2 x) d x

\frac{\partial}{\partial x} (sin (4 x))

\frac{d}{d x} (\frac{7 x}{x ^{2} + 4})

d er i v a t i v e \frac{1}{6} x^{3} + \frac{1}{2 x}

\frac{d}{d x} (4 + 3 f (x))