Consider the ODE for u(x) defined over the interval, p<x<q, \frac{d^{2} u}{d x^{2}}=1 with boundary conditions u^{\prime}(p)=P \quad, u^{\prime}(q)=Q where u' denotes du/dx. As mentioned in Lecture 3, the existence and uniqueness of the solution(s)for the system generally depend on the values of (p, q, P, Q). (i) Find an example of the values of (p, q, P, Q) for which the system has a unique solution. If you determine that it is not possible for the system to have a unique solution, please explain why. (ii) Find an example of the values of (p, q, P, Q) for which the system has no solution at all. Ifyou determine that the system always has a solution (or solutions), please explain why. (iii) Find an example of the values of (p, q, P, Q) for which the system has multiple solutions. (Inother words, the solutions for the system exist but are not unique.) If you determine that it is not

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Consider the ODE for u(x) defined over the interval, p<x<q, \frac{d^{2} u}{d x^{2}}=1 with boundary conditions u^{\prime}(p)=P \quad, u^{\prime}(q)=Q where u' denotes du/dx. As mentioned in Lecture 3, the existence and uniqueness of the solution(s)for the system generally depend on the values of (p, q, P, Q). (i) Find