erweitern x^2y''(x)+x(x+2)y'(x)-(x+2)y

Lösung

erweitern

x^{2} y^{''} (x) + x (x + 2) y^{'} (x) - (x + 2) y

x^{2} y'' (x) + x^{2} y' (x) + 2 x y' (x) - x y - 2 y

Schritte zur Lösung

x^{2} y^{''} (x) + x (x + 2) y^{'} (x) - (x + 2) y

Multipliziere aus

x y^{'} (x) (x + 2) : x^{2} y^{'} (x) + 2 x y^{'} (x)

= x^{2} y^{''} (x) + x^{2} y^{'} (x) + 2 x y^{'} (x) - (x + 2) y

Multipliziere aus

- y (x + 2) : - x y - 2 y

= x^{2} y^{''} (x) + x^{2} y^{'} (x) + 2 x y^{'} (x) - x y - 2 y

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

s im pl i f y i x (i x + 3) (i x + 6)

e x p an d - \frac{4 - x ^{2}}{( 4 + x ^{2} ) ^{2}}

e x p an d (x e^{a x}) (e^{b x} + b e^{b x} x)

e x p an d \frac{t ( t - 2 )}{( 1 + t ) ( 1 - t )}