59.1.118 problem 120

Internal problem ID [9290]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 120
Date solved : Monday, January 27, 2025 at 06:01:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 23

dsolve(4*x^2*(1+3*x+x^2)*diff(y(x),x$2)-4*x*(1-3*x-3*x^2)*diff(y(x),x)+3*(1-x+x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {\sqrt {x}\, \left (c_{2} x +c_{1} \right )}{x^{2}+3 x +1} \]

✓ Solution by Mathematica

Time used: 0.182 (sec). Leaf size: 52

DSolve[4*x^2*(1+3*x+x^2)*D[y[x],{x,2}]-4*x*(1-3*x-3*x^2)*D[y[x],x]+3*(1-x+x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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