59.2.5 problem 5

Internal problem ID [9998]
Book : Collection of Kovacic problems
Section : section 2. Solution found using all possible Kovacic cases
Problem number : 5
Date solved : Monday, January 27, 2025 at 06:16:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

\[ y = {\mathrm e}^{x} \left (c_{2} x^{3}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 25

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

\[ y(x)\to \frac {1}{3} e^{x+1} \left (c_2 x^3+3 c_1\right ) \]