se a,b,c e k são constantes: mostre que se W= ( a cos (cx) + b sen (cx) ) e^-kte^2 . então dw/dt =d^2w/dx^2.

W=(a*cos (cx) + B*sen(cx))*(e^(-kt))*e² 

é isso que voce quis dizer?

\(\[\begin{align} & W=(a.cos(cx)+B.sen(cx)).({{e}^{(-kt)}}).e{}^\text{2} \\ & f\left( x+T \right)\text{ }=\text{ }f\left( x \right) \\ & cos\left( x \right)=cos\left( x+2pi \right)=cos\left( x+4pi \right) \\ & =cos\left( x+2kpi \right) \\ & cos\left( x+2kpi \right)= \\ & cos\left( x \right)\text{ }cos\left( 2kpi \right)sen\left( x \right)\text{ }sen\left( 2kpi \right) \\ & cos\left( x+2kpi \right)= \\ & cos\left( x \right)\text{ }\left( 1 \right)sen\left( x \right)\text{ }\left( 0 \right)=cos\left( x \right) \\ & 1<cos\left( x \right)<1 \\ & cos\left( x \right)\text{ }=\text{ }cos\left( x \right) \\ \end{align}\] \)