erweitern (y^3(ydx+xdy)-(ydx-xdy)=0) 1/(y^2)

Lösung

erweitern

(y^{3} (y d x + x d y) - (y d x - x d y) = 0) \frac{1}{y ^{2}}

y^{2} d x + y x d y - \frac{d x}{y} + \frac{x d y}{y ^{2}} = 0

Schritte zur Lösung

(y^{3} (y d x + x d y) - (y d x - x d y) = 0) \frac{1}{y ^{2}}

= \frac{1}{y ^{2}} (y^{3} (y d x + x d y) - 0 = (y d x - x d y))

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = \frac{1}{y ^{2}}, b = y^{3} (y d x + x d y), c = (y d x - x d y) = 0

\frac{1}{y ^{2}} y^{3} (y d x + x d y) - \frac{1}{y ^{2}} (y d x - x d y) = 0

Multipliziere aus

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

y^{2} d x + y x d y - \frac{d x}{y} + \frac{x d y}{y ^{2}} = 0

e x p an d x ln^{2} (x) - 2 (x ln (x) - x)

e x p an d (sin^{4} (x) + cos^{4} (x - 1)) (sec^{2} (x) + csc^{2} (x))

e x p an d \frac{0.714 ( x ^{2} + 1.39 x + 1274209.9 )}{x ( x + 1.59 ) ( x ^{2} + 1.06 x + 1274212.3 )}

e x p an d - \frac{36 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

e x p an d \frac{( 6 - x ) ^{4}}{81}