37.3.7 problem 10.4.8 (g)

Internal problem ID [6413]
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)
Date solved : Monday, January 27, 2025 at 02:00:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+x y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 28

dsolve(x*diff(y(x),x$2)+x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
 

\[ y = -\frac {\left (x +1\right ) c_2 \,{\mathrm e}^{-x}}{2}+x \left (c_1 +\frac {c_2 \,\operatorname {Ei}_{1}\left (x \right )}{2}\right ) \left (x +2\right ) \]

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 39

DSolve[x*D[y[x],{x,2}]+x*D[y[x],x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 x (x+2)-\frac {1}{2} c_2 e^{-x} \left (e^x (x+2) x \operatorname {ExpIntegralEi}(-x)+x+1\right ) \]