(d^2)/(dx^2)((y)(e^{2x}-kx))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (e^{2 x} - k x))

\frac{d ^{2} y}{d x ^{2}} (e^{2 x} - k x) + 2 \frac{d y}{d x} (2 e^{2 x} - k) + 4 e^{2 x} y

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (e^{2 x} - k x))

\frac{d}{d x} (y (e^{2 x} - k x)) = \frac{d y}{d x} (e^{2 x} - k x) + (e^{2 x} \cdot 2 - k) y

= \frac{d}{d x} (\frac{d y}{d x} (e^{2 x} - k x) + (e^{2 x} \cdot 2 - k) y)

\frac{d}{d x} (\frac{d y}{d x} (e^{2 x} - k x) + (e^{2 x} \cdot 2 - k) y) = \frac{d ^{2} y}{d x ^{2}} (e^{2 x} - k x) + 2 \frac{d y}{d x} (2 e^{2 x} - k) + 4 e^{2 x} y

= \frac{d ^{2} y}{d x ^{2}} (e^{2 x} - k x) + 2 \frac{d y}{d x} (2 e^{2 x} - k) + 4 e^{2 x} y

e x p an d (c_{1} x + c_{2} e^{- 2 x}) e^{2 x}

e x p an d \frac{6}{( s - 1 ) ^{2}}

e x p an d (5 cot (x) + 4)^{2}

e x p an d \frac{35 x + 23}{( x ^{3} + 1 ) ( x - 1 )}

e x p an d (x + 5) l e f t (x + 2)