(d^2)/(dx^2)((y)(cos(5x)-4))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (cos (5 x) - 4))

cos (5 x) \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d ^{2} y}{d x ^{2}} - 10 sin (5 x) \frac{d y}{d x} - 25 cos (5 x) y

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (cos (5 x) - 4))

\frac{d}{d x} (y (cos (5 x) - 4)) = \frac{d y}{d x} (cos (5 x) - 4) - 5 sin (5 x) y

= \frac{d}{d x} (\frac{d y}{d x} (cos (5 x) - 4) - 5 sin (5 x) y)

\frac{d}{d x} (\frac{d y}{d x} (cos (5 x) - 4) - 5 sin (5 x) y) = cos (5 x) \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d ^{2} y}{d x ^{2}} - 10 sin (5 x) \frac{d y}{d x} - 25 cos (5 x) y

= cos (5 x) \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d ^{2} y}{d x ^{2}} - 10 sin (5 x) \frac{d y}{d x} - 25 cos (5 x) y

e x p an d \frac{507}{s ( s ^{2} - 4 s + 13 ) ^{2}}

e x p an d \frac{1}{( x ^{2} - A ) ( x ^{2} - B )}

e x p an d (x + 2) ln (x + 2)

e x p an d \frac{x ^{2} ( x - 3 )}{x + 4}

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