(dy)/(dx)=(x/(y-2))^{{3}}ln(2x)

Lösung

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

y = 4 \frac{4 x ^{4} ln ( 2 x ) - x ^{4} + c _{1}}{4} + 2, y = - 4 \frac{4 x ^{4} ln ( 2 x ) - x ^{4} + c _{1}}{4} + 2

Schritte zur Lösung

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

Solve separable ODE:

y = 4 \frac{4 x ^{4} ln ( 2 x ) - x ^{4} + c _{1}}{4} + 2, y = - 4 \frac{4 x ^{4} ln ( 2 x ) - x ^{4} + c _{1}}{4} + 2

y = 4 \frac{4 x ^{4} ln ( 2 x ) - x ^{4} + c _{1}}{4} + 2, y = - 4 \frac{4 x ^{4} ln ( 2 x ) - x ^{4} + c _{1}}{4} + 2

\int_{0}^{\infty} x^{4} e^{- x} d x

\frac{d}{d x} (e^{2 x} - e^{x} + 1)

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

\frac{d}{d x} (\frac{1}{a ^{2} + x ^{2}})

\frac{d}{d x} (sin^{2} (\frac{x}{x + 1}))