59.1.284 problem 287

Internal problem ID [9456]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 287
Date solved : Monday, January 27, 2025 at 06:03:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.184 (sec). Leaf size: 100

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

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