y=(e^t)cost
y'=(e^t)(cost-sint)
y''=(e^t)(cost-sint)+(e^t)(-cost-sint)
=(e^t)(-2sint)
x=(e^t)sint
x'=(e^t)(sint+cost)
x''=(e^t)(sint+cost)+(e^t)(-sint+cost)
=(e^t)(2cost)
左边=y''(x+y)^2 =(e^t)(-2sint)*（(e^t)(sint+cost)）²=-2e^3t*sint(1+sin2t)
右边=2(xy'-y)=2((e^t)sint*(e^t)(cost-sint)-(e^t)cost )。很高兴为你解答，有啥不懂的随时都可以再问我
