But here is the open secret every senior tells the fresher: You cannot pass without the solution manual.
The best engineers don't memorize the solution to ( (D^2 + 4)y = \tan(2x) ). They memorize the method of variation of parameters so they can solve any weird forcing function the real world throws at them. Advanced Engineering Mathematics H K Dass Solution
The H.K. Dass solution will spend 80% of its time doing partial derivatives, line integrals, and determinant expansions. It will give you a numeric answer (e.g., LHS = 5, RHS = 5. Verified). But here is the open secret every senior