59.1.231 problem 234

Internal problem ID [9403]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 234
Date solved : Monday, January 27, 2025 at 06:02:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 32

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

\[ y = \frac {c_{1} x^{2} \left (4 x^{2}-36 x +63\right )}{63}+\frac {c_{2} \operatorname {hypergeom}\left (\left [-\frac {9}{2}\right ], \left [-\frac {3}{2}\right ], x\right )}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 1.857 (sec). Leaf size: 61

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

\[ y(x)\to \frac {1}{4} x^2 \left (4 x^2-36 x+63\right ) \left (c_2 \int _1^x\frac {16 e^{K[1]}}{K[1]^{7/2} \left (4 K[1]^2-36 K[1]+63\right )^2}dK[1]+c_1\right ) \]