Chapter 4.1, Problem 14E

In Problems 13 and 14 the given two-parameter family is a solution of the indicated differential equation on the interval (−∞, ∞). Determine whether a member of the family can be found that satisfies the boundary conditions.

14. $y=c_1{x}^2+c_2{x}^4+3;x^2{y}^{″}-5x{y}^{\prime }+8y=24$

$\begin{array}{l}\begin{array}{ccc}(a)& y(-1)=0,& y(1)\end{array}=4\\ \begin{array}{ccc}(b)& y(0)=1,& y(1)=2\end{array}\\ \begin{array}{ccc}(c)& y(0)=3,& y(1)=0\end{array}\\ \begin{array}{ccc}(d)& y(1)=3,& y(2)=15\end{array}\end{array}$