erweitern ycos(t)+2te^y(sin(t)+t^2e^y+2)(dy)/(dt)

Lösung

erweitern

y cos (t) + 2 t e^{y} (sin (t) + t^{2} e^{y} + 2) \frac{d y}{d t}

y cos (t) + 2 e^{y} t sin (t) \frac{d y}{d t} + 2 e^{2 y} t^{3} \frac{d y}{d t} + 4 e^{y} t \frac{d y}{d t}

Schritte zur Lösung

y cos (t) + 2 t e^{y} (sin (t) + t^{2} e^{y} + 2) \frac{d y}{d t}

= cos (t) y + 2 e^{y} t (sin (t) + e^{y} t^{2} + 2) \frac{d y}{d t}

Multipliziere aus

2 t e^{y} \frac{d y}{d t} (sin (t) + t^{2} e^{y} + 2) : 2 e^{y} t sin (t) \frac{d y}{d t} + 2 e^{2 y} t^{3} \frac{d y}{d t} + 4 e^{y} t \frac{d y}{d t}

= y cos (t) + 2 e^{y} t sin (t) \frac{d y}{d t} + 2 e^{2 y} t^{3} \frac{d y}{d t} + 4 e^{y} t \frac{d y}{d t}

e x p an d \frac{x ^{2} + 4 x + 5}{( x - 5 ) ( x + 5 )}

e x p an d 2 (y - x) d x + x (2 y - x + 2) d y

e x p an d - \frac{16 ln ( 3 )}{25 ( 1 - e ^{\frac{2 l n ( 3 )}{25}} )}

s im pl i f y ((\frac{2}{x - 12}) + 9 (100 - x)) (x - 4)

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