59.1.97 problem 99

Internal problem ID [9269]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 99
Date solved : Monday, January 27, 2025 at 06:00:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 19

dsolve(2*x^2*(2+3*x)*diff(y(x),x$2)+x*(4+11*x)*diff(y(x),x)-(1-x)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} \left (2+3 x \right )^{{1}/{6}}+c_{1}}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.323 (sec). Leaf size: 69

DSolve[2*x^2*(2+3*x)*D[y[x],{x,2}]+x*(4+11*x)*D[y[x],x]-(1-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt [6]{2} (3 x+2)^{5/12} \left (c_2 \sqrt [6]{3 x+2}+2^{2/3} c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {5}{6 K[1]+4}+\frac {1}{K[1]}\right )dK[1]\right ) \]