(dy)/(dx)=((2y+1)/(4x-3))^2

Lösung

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

y = - \frac{4 x}{- 1 + 16 c _{1} x - 12 c _{1}} - \frac{8 c _{1} x}{- 1 + 16 c _{1} x - 12 c _{1}} + \frac{6 c _{1}}{- 1 + 16 c _{1} x - 12 c _{1}} + \frac{7}{2 ( - 1 + 16 c _{1} x - 12 c _{1} )}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{4 x}{- 1 + 16 c _{1} x - 12 c _{1}} - \frac{8 c _{1} x}{- 1 + 16 c _{1} x - 12 c _{1}} + \frac{6 c _{1}}{- 1 + 16 c _{1} x - 12 c _{1}} + \frac{7}{2 ( - 1 + 16 c _{1} x - 12 c _{1} )}

y = - \frac{4 x}{- 1 + 16 c _{1} x - 12 c _{1}} - \frac{8 c _{1} x}{- 1 + 16 c _{1} x - 12 c _{1}} + \frac{6 c _{1}}{- 1 + 16 c _{1} x - 12 c _{1}} + \frac{7}{2 ( - 1 + 16 c _{1} x - 12 c _{1} )}

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

\int_{0}^{\frac{π}{4}} sin^{2} (2 x) d x

d er i v a t i v e f (x) = ln (sin (x))

d er i v a t i v e 15 x \cdot ln (20 x)

x \to 1 lim ((x^{2} - 9)^{\frac{1}{3}})