Determine whether the given function is a solution to the given differential equation.

1. x = 2 cos t - 3 sin t, x" + x = 0

2. y = sin x + x^2, d^2y/dx^2 + y = x^2 + 2

3. x = cos 2t, dx/dt + tx = sin 2t

It is only 1 and 2 that is the solution to the differential equation

Step-by-step explanation:

1. x'' = - 2 Cos t + 3 sin t and x=2 cos t - 3 sin t the addition give 0

2. d^2y/dx^2 = - Sin x + 2 and y = Sin x + x^2 the addition = x^2+2

but

3. dx/dt = - 2 Sin 2t and tx = t Cos 2t = t (2Cos t - 2 Sin t) the addition it can't equal Sin 2t