Internal problem ID [4349]
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: 22.
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 }+x y^{\prime }+y-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 16
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=2*x,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (\ln \relax (x )\right ) c_{2}+\cos \left (\ln \relax (x )\right ) c_{1}+x \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 19
DSolve[x^2*y''[x]+x*y'[x]+y[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+c_1 \cos (\log (x))+c_2 \sin (\log (x)) \\ \end{align*}