59.1.33 problem 34

Internal problem ID [9205]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 34
Date solved : Monday, January 27, 2025 at 05:52:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

dsolve((2*x+1)*diff(y(x),x$2)-2*diff(y(x),x)-(2*x+3)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-x}+c_{2} {\mathrm e}^{x} x \]

✓ Solution by Mathematica

Time used: 0.358 (sec). Leaf size: 69

DSolve[(2*x+1)*D[y[x],{x,2}]-2*D[y[x],x]-(2*x+3)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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