59.1.302 problem 305

Internal problem ID [9474]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 305
Date solved : Monday, January 27, 2025 at 06:03:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

\[ y = \sqrt {x}\, c_{1} +c_{2} \sqrt {x \left (x -2\right )} \]

✓ Solution by Mathematica

Time used: 0.299 (sec). Leaf size: 57

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

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