?For each of the following problems, verify that the given function is a solution to the
Chapter 7, Problem 8(choose chapter or problem)
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 \(c_{1}\) and \(c_{2}\). What do the solutions have in common?
[T] \(x^{2} y^{\prime \prime}-2 y-3 x^{2}+1=0\); \(y(x)=c_{1} x^{2}+c_{2} x^{-1}+x^{2} \ln (x)+\frac{1}{2}\)
Text Transcription:
x^{2} y^{\prime \prime}-2 y-3 x^{2}+1=0
y(x)=c_{1} x^{2}+c_{2} x^{-1}+x^{2} \ln (x)+\frac{1}{2}
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