59.1.421 problem 433

Internal problem ID [9593]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 433
Date solved : Monday, January 27, 2025 at 06:04:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve((1+x^2)*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = c_{2} x^{3}-3 c_{1} x^{2}-3 c_{2} x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.253 (sec). Leaf size: 75

DSolve[(1+x^2)*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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