9/10 x^2dy-18dx=0

Lösung

\frac{9}{10} x^{2} d y - 18 d x = 0

y = - \frac{20}{x} + c_{1}

Schritte zur Lösung

\frac{9}{10} x^{2} d y - 18 d x = 0

Lass

y

die abhängige Variable sein. Teile durch

d x

\frac{9}{10} x^{2} \frac{d y}{d x} - 18 = 0

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

\frac{9}{10} x^{2} y^{^{'}} (x) - 18 = 0

Isoliere

y^{'} (x) : y^{'} (x) = \frac{20}{x ^{2}}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

y = \int \frac{20}{x ^{2}} d x

\int \frac{20}{x ^{2}} d x = - \frac{20}{x} + c_{1}

y = - \frac{20}{x} + c_{1}

\frac{\partial}{\partial x} (x^{3} + x^{2} y - y^{2} - 4 y)

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

x \to 5 + lim (\frac{2}{x + 5})

\frac{\partial}{\partial x} (a x + b y^{2} + c x^{2} y)

\frac{d}{d x} (arctan (tan (x)))