Since y = e^{x }(sinx + cosx)

dy/dx = e^{x }(sinx + cosx) +e^{x }(cosx - sinx)

dy/dx = y + e^{x }(cosx - sinx)

d^{2}y/ dx^{2 }= dy/dx + e^{x }(cosx - sinx) +e^{x}(-sinx - cosx)

d^{2}y/dx^{2 }= dy/dx + dy/dx - y - y

d^{2}y/dx^{2 }= 2dy/dx -2y

d^{2}y/dx^{2} - 2dy/dx + 2y = 0

Hence proved