Internal problem ID [4562]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.4, ODEs with variable Coefficients. Second
order and Homogeneous. page 318
Problem number: 10.4.8 (g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+x y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 37
dsolve(x*diff(y(x),x$2)+x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x^{2}+2 x \right )+c_{2} \left (\frac {\left (-x -1\right ) {\mathrm e}^{-x}}{2}+\frac {x \expIntegral \left (1, x\right ) \left (x +2\right )}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 39
DSolve[x*y''[x]+x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x (x+2)-\frac {1}{2} c_2 e^{-x} \left (e^x (x+2) x \text {ExpIntegralEi}(-x)+x+1\right ) \\ \end{align*}