1.729 problem 744

Internal problem ID [7463]

Book: Collection of Kovacic problems
Section: section 1
Problem number: 744.
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: 0.016 (sec). Leaf size: 38

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

\[ y \relax (x ) = c_{1} \left (x^{2}+2 x \right )+c_{2} \left (\frac {\left (x^{2}+2 x \right ) \expIntegral \left (1, x\right )}{2}-\frac {\left (x +1\right ) {\mathrm e}^{-x}}{2}\right ) \]

Solution by Mathematica

Time used: 0.054 (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 {Ei}(-x)+x+1\right ) \\ \end{align*}