Internal problem ID [2299]
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 20.
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-\frac {x^{2}}{\ln \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
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)
\[ y \relax (x ) = x^{2} c_{2}+\ln \relax (x ) c_{1} x^{2}+\ln \relax (x ) x^{2} \left (\ln \left (\ln \relax (x )\right )-1\right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 24
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 x^2 (\log (x) (\log (\log (x))-1+2 c_2)+c_1) \\ \end{align*}