Problem $2$: Principle of Superposition $8$ points

In the following subproblems, $,,$ and $$ are parameters:

$1.$ Prove by substitution that $()=$ is a solution to $()+()=$

$2.$ Prove by substitution that $()=$

$(1)$ is a solution to $()+()=$

$3.$ Using the above two results, determine the solution to $()+3()=43+1/3$