59.1.750 problem 772

Internal problem ID [9922]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 772
Date solved : Monday, January 27, 2025 at 06:15:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.329 (sec). Leaf size: 73

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

\[ y = \frac {c_{2} \sqrt {\frac {\left (-2 \sqrt {x}+i\right ) \left (4 x +1\right )}{2 \sqrt {x}+i}}\, {\mathrm e}^{-2 i \sqrt {x}}+c_{1} \sqrt {\frac {\left (2 \sqrt {x}+i\right ) \left (4 x +1\right )}{-2 \sqrt {x}+i}}\, {\mathrm e}^{2 i \sqrt {x}}}{x} \]

✓ Solution by Mathematica

Time used: 0.213 (sec). Leaf size: 77

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

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