59.1.598 problem 614

Internal problem ID [9770]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 614
Date solved : Monday, January 27, 2025 at 06:14:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 45

dsolve(x^2*(1+x)*diff(y(x),x$2)+3*x^2*diff(y(x),x)-(6-x)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} \left (x +4\right )+\frac {c_{2} \left (6 \left (x +4\right ) \left (x +1\right )^{2} \ln \left (x +1\right )+60 x^{2}+129 x +68\right )}{\left (x +1\right )^{2}}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.474 (sec). Leaf size: 91

DSolve[x^2*(1+x)*D[y[x],{x,2}]+3*x^2*D[y[x],x]-(6-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {(x+4) \exp \left (\int _1^x\left (\frac {3}{2 (K[1]+1)}-\frac {2}{K[1]}\right )dK[1]\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[2]}\left (\frac {3}{2 (K[1]+1)}-\frac {2}{K[1]}\right )dK[1]\right )}{(K[2]+4)^2}dK[2]+c_1\right )}{(x+1)^{3/2}} \]