59.1.72 problem 74

Internal problem ID [9244]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 74
Date solved : Monday, January 27, 2025 at 06:00:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.147 (sec). Leaf size: 31

dsolve((3*x+2*x^2)*diff(y(x),x$2)+10*(1+x)*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \left (x +2\right )}{\left (1+\frac {2 x}{3}\right )^{{2}/{3}} x^{{7}/{3}}}+c_{2} \operatorname {hypergeom}\left (\left [2, 2\right ], \left [\frac {10}{3}\right ], -\frac {2 x}{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.439 (sec). Leaf size: 118

DSolve[(3*x+2*x^2)*D[y[x],{x,2}]+10*(1+x)*D[y[x],x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x+2) \exp \left (\int _1^x-\frac {K[1]+2}{2 K[1]^2+3 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {10 (K[2]+1)}{K[2] (2 K[2]+3)}dK[2]\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[3]}-\frac {K[1]+2}{2 K[1]^2+3 K[1]}dK[1]\right )}{(K[3]+2)^2}dK[3]+c_1\right ) \]