Internal problem ID [2296]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.8, A Differential Equation with
Nonconstant Coefficients. page 567
Problem number: Problem 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +5 y-8 x \ln \relax (x )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 31
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+5*y(x)=8*x*(ln(x))^2,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 \ln \relax (x )\right ) x c_{2}+\cos \left (2 \ln \relax (x )\right ) x c_{1}+2 \ln \relax (x )^{2} x -x \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 31
DSolve[x^2*y''[x]-x*y'[x]+5*y[x]==8*x*(Log[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (2 \log ^2(x)+c_2 \cos (2 \log (x))+c_1 \sin (2 \log (x))-1\right ) \\ \end{align*}