59.1.117 problem 119

Internal problem ID [9289]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 119
Date solved : Monday, January 27, 2025 at 06:01:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 22

dsolve(8*x^2*(2-x^2)*diff(y(x),x$2)+2*x*(10-21*x^2)*diff(y(x),x)-(2+35*x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} x^{{3}/{4}}+c_{1}}{\left (x^{2}-2\right ) \sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.270 (sec). Leaf size: 62

DSolve[8*x^2*(2-x^2)*D[y[x],{x,2}]+2*x*(10-21*x^2)*D[y[x],x]-(2+35*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} \sqrt [8]{x} \left (4 c_2 x^{3/4}+3 c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {4 K[1]}{K[1]^2-2}+\frac {5}{4 K[1]}\right )dK[1]\right ) \]