That is the only solution that truly matters.
A solution manual, used wisely, is not a crutch—it is a tutor that works for free at 2 AM. But a solution manual cannot think for you during an exam. As you work through Serway’s iconic problems (the muon decay, the Compton scattering off graphite, the infinite square well perturbation), remember: every physicist who came before you struggled with these exact same equations. modern physics serway 3rd edition solutions
Did you set up the integral correctly for a particle in a 1D box? That is the only solution that truly matters