Check that the indicated variable changes transform the corresponding Partial differential equations into u(x, t) to the Partial differential equations in w(x, t)

a). u,(x,t)= au(x,t) Bu( x,t );u(x,t)=ew(x,t);w;(x,1) = a'w(x,t) b). u,(x,1) = a'u (x,1)-yu,(x,1);u(x,1) = e(*-1/2)/2a w(x,t);w,(x,t)= a*w(x,t)