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

解答

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

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

求解步骤

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

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

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

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

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

e x p an d (- 7 - 3) (- 7 + 2)

e x p an d 7 (x + Δ x)^{2}

e x p an d e^{x} (e^{1 + x} - e^{- 1 - x})

e x p an d \frac{1}{60} \cdot 8 - \frac{1}{4} \cdot 4 + \frac{37}{30} \cdot 2

e x p an d ((2 x^{2} y - 2 y^{2} + 2 x y) d x + (x^{2} - 2 y) d y = 0) e^{2 x}