59.1.90 problem 92

Internal problem ID [9262]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 92
Date solved : Monday, January 27, 2025 at 06:00:42 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 41

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

\[ y(x)\to \frac {1}{2} e^{-2 \sqrt {x}} \sqrt {x} \left (2 c_1 e^{4 \sqrt {x}}-c_2\right ) \]