Internal problem ID [4347]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page
435
Problem number: 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 x y^{\prime }+4 y-6 x^{2} \ln \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 25
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=6*x^2*ln(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} x^{2}+c_{1} x^{2} \ln \relax (x )+\ln \relax (x )^{3} x^{2} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 22
DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x]==6*x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 \left (\log ^3(x)+2 c_2 \log (x)+c_1\right ) \\ \end{align*}