Chapter 8.6, Problem 37P

In Problem 33 to 38, solve the given differential equations by using the principle of superposition [see the solution of equation (6.29)]. For example, in Problem 33, solve three differential equations with right-hand sides equal to the three different brackets. Note that terms with the same exponential factor are kept together; thus a polynomial of any degree is kept together in one bracket.

${(D-1)}^{2}y=4e^x+(1-x)\left(e^{2x}-1\right)$