erweitern (y''(t)+2y'(t)+2)^2

Lösung

erweitern

(y^{''} (t) + 2 y^{'} (t) + 2)^{2}

4 y' (t) y'' (t) + 4 (y' (t))^{2} + 8 y' (t) + (y'' (t))^{2} + 4 y'' (t) + 4

Schritte zur Lösung

(y^{''} (t) + 2 y^{'} (t) + 2)^{2}

(y^{''} (t) + 2 y^{'} (t) + 2)^{2} = (y^{''} (t) + 2 y^{'} (t) + 2) (y^{''} (t) + 2 y^{'} (t) + 2)

= (y^{^{''}} (t) + 2 y^{^{'}} (t) + 2) (y^{^{''}} (t) + 2 y^{^{'}} (t) + 2)

Multipliziere aus

(y^{''} (t) + 2 y^{'} (t) + 2) (y^{''} (t) + 2 y^{'} (t) + 2) : 4 y^{'} (t) y^{''} (t) + 4 (y^{'} (t))^{2} + 8 y^{'} (t) + (y^{''} (t))^{2} + 4 y^{''} (t) + 4

= 4 y^{'} (t) y^{''} (t) + 4 (y^{'} (t))^{2} + 8 y^{'} (t) + (y^{''} (t))^{2} + 4 y^{''} (t) + 4

e x p an d cos (θ) cot (θ) (sec (θ) - 2 tan (θ))

e x p an d tan (x) (1 - sin (2 x)) sec (x)

e x p an d \frac{3 x}{sin ( x ) ( x - 3 )}

e x p an d \frac{1}{4 ( 8 x + 12 )}

s im pl i f y 2 (\frac{y}{3} + 1)