Chapter 7.1, Problem 8E

For each of the following problems, verify that the given function is a solution to the differential equation. Use a graphing utility to graph the particular solutions for several values of c₁and c₂. What do the solutions have in common?

8. [T] $x^2{y}^{″}-2y-3x^2+1=0$ ; $y\left(x\right)=c_1{x}^2+c_2{x}^{-1}+x^{2}In\left(x\right)+\frac{1}{2}$