Internal problem ID [2112]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 47.
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 }-3 y^{\prime } x +4 y-\ln \relax (x ) x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 26
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=x^2*ln(x),y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{2}+\ln \relax (x ) c_{1} x^{2}+\frac {\ln \relax (x )^{3} x^{2}}{6} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 27
DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x]==x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} x^2 \left (\log ^3(x)+12 c_2 \log (x)+6 c_1\right ) \\ \end{align*}