59.1.75 problem 77

Internal problem ID [9247]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 77
Date solved : Monday, January 27, 2025 at 06:00:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 33

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

\[ y = \left (\left (x^{2}+3 x +9\right ) \left (x^{2}+9 x +27\right ) \left (6+x \right ) c_{2} x +c_{1} \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.329 (sec). Leaf size: 52

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

\[ y(x)\to \frac {\left (c_2 (x+3)^6+6 c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (2-\frac {5}{K[1]+3}\right )dK[1]\right )}{6 (x+3)^{5/2}} \]