implicit (dy)/(dx),e^{x/y}=x-y

Lösung

implizite ableitung

\frac{d y}{d x}, e^{\frac{x}{y}} = x - y

\frac{d y}{d x} = \frac{y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

Schritte zur Lösung

e^{\frac{x}{y}} = x - y

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

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

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

\frac{d y}{d x} = \frac{y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

\int 9 y d y

\int \frac{2}{3} x^{- \frac{1}{3}} d x

v o l u m e ab o u t y = 0, y = ln (x), y = 0, [1, 2]

\frac{d y}{d x} = - 9.81 + 0.00375 y^{2}

l a pl a ce t r an s f or m e^{- 3 t} cos (- t)