59.1.114 problem 116

Internal problem ID [9286]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 116
Date solved : Monday, January 27, 2025 at 06:01:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.234 (sec). Leaf size: 53

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

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