Determine if the function y = x + 2 is a solution to the IVP
The initial condition holds:
y(0) = (0) + 2 = 2.
The left-hand side of the d.e. is
2y = 2(x + 2) = 2x + 4.
Since the derivative of y is 1, the right-hand side of the d.e. is
Since the two sides of the d.e. are not equal, the function y = x + 2 is not a solution to the d.e. and therefore can't be a solution to the IVP either.