Internal problem ID [4345]
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: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }-y-x +\frac {1}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 31
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=x-1/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}+c_{2} x +\frac {2 \ln \relax (x ) x^{2}+2 \ln \relax (x )+1}{4 x} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 37
DSolve[x^2*y''[x]+x*y'[x]-y[x]==x-1/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 \left (x^2+1\right ) \log (x)+(-1+4 c_2) x^2+1+4 c_1}{4 x} \\ \end{align*}