Internal problem ID [4139]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22, problem 17, page 240.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}}-x \ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-2/x*diff(y(x),x)+2/x^2*y(x)=x*ln(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} x^{2}+\frac {x^{3} \left (2 \ln \relax (x )-3\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 32
DSolve[y''[x]-2/x*y'[x]+2/x^2*y[x]==x*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x \left (-3 x^2+2 x^2 \log (x)+4 c_2 x+4 c_1\right ) \\ \end{align*}