1.747 problem 763

Internal problem ID [8237]

Book: Collection of Kovacic problems
Section: section 1
Problem number: 763.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

\[ \boxed {\left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y=0} \]

Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

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

\[ y \left (x \right ) = x c_{1} +c_{2} {\mathrm e}^{-x} \left (x +4\right ) \]

Solution by Mathematica

Time used: 0.14 (sec). Leaf size: 72

DSolve[(x+2)*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {2 \sqrt {\frac {2}{\pi }} e^{-x-2} \sqrt {x+2} \left (c_1 \left (e^{x+2} x+x+4\right )-i c_2 \left (\left (e^{x+2}-1\right ) x-4\right )\right )}{\sqrt {-i (x+2)}} \]