Internal problem ID [256]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 61.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +y-\ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=ln(x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (\ln \relax (x )\right ) c_{2}+\cos \left (\ln \relax (x )\right ) c_{1}+\ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 20
DSolve[x^2*y''[x]+x*y'[x]+y[x]==Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log (x)+c_1 \cos (\log (x))+c_2 \sin (\log (x)) \\ \end{align*}