(d^2)/(dx^2)((y)(x-1/2 sin(x)))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (x - \frac{1}{2} sin (x)))

x \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + \frac{- 2 cos ( x ) \frac{d y}{d x} - sin ( x ) \frac{d ^{2} y}{d x ^{2}} + sin ( x ) y}{2}

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (x - \frac{1}{2} sin (x)))

\frac{d}{d x} (y (x - \frac{1}{2} sin (x))) = x \frac{d y}{d x} + \frac{- sin ( x ) \frac{d y}{d x} - cos ( x ) y}{2} + y

= \frac{d}{d x} (x \frac{d y}{d x} + \frac{- sin ( x ) \frac{d y}{d x} - cos ( x ) y}{2} + y)

\frac{d}{d x} (x \frac{d y}{d x} + \frac{- sin ( x ) \frac{d y}{d x} - cos ( x ) y}{2} + y) = x \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + \frac{- 2 cos ( x ) \frac{d y}{d x} - sin ( x ) \frac{d ^{2} y}{d x ^{2}} + sin ( x ) y}{2}

= x \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + \frac{- 2 cos ( x ) \frac{d y}{d x} - sin ( x ) \frac{d ^{2} y}{d x ^{2}} + sin ( x ) y}{2}

e x p an d \frac{a ( a ^{5} - a b ^{2} + b ^{3} )}{b}

e x p an d \frac{s + 8}{( s + 3 ) ( s + 6 ) ( s + 10 )}

s im pl i f y (cos (x)) (1 - sin (x))

e x p an d \frac{8}{( x + 2 ) ( x - 2 )}

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