59.1.395 problem 407

Internal problem ID [9567]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 407
Date solved : Monday, January 27, 2025 at 06:04:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (1+x \right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

dsolve((x+1)*diff(y(x),x$2)-(x+2)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.208 (sec). Leaf size: 84

DSolve[(x+1)*D[y[x],{x,2}]-(x+2)*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {K[1]}{2 K[1]+2}dK[1]-\frac {1}{2} \int _1^x\left (-1-\frac {1}{K[2]+1}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {K[1]}{2 K[1]+2}dK[1]\right )dK[3]+c_1\right ) \]