Determine if the function y = x2 + 4x is a solution to the IVP
The initial condition is satisfied:
y(1) = (1)2 + 4(1) = 5.
The left-hand side of the d.e. is
The right-hand side of the d.e. is
Since the two sides of the d.e. are the same, this function is a solution to the differential equation. Since this function also satisfies the initial condition, the function y = x2 + 4x is a solution to the IVP.