59.1.254 problem 257

Internal problem ID [9426]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 257
Date solved : Monday, January 27, 2025 at 06:02:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 44

dsolve(2*x*diff(y(x),x$2)+5*(1-2*x)*diff(y(x),x)-5*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {10 \sqrt {5}\, c_{1} \sqrt {\pi }\, \left (\frac {1}{10}+x \right ) \operatorname {erfi}\left (\sqrt {5}\, \sqrt {x}\right )-10 \,{\mathrm e}^{5 x} c_{1} \sqrt {x}+10 c_{2} \left (\frac {1}{10}+x \right )}{x^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 40

DSolve[2*x*D[y[x],{x,2}]+5*(1-2*x)*D[y[x],x]-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 L_{-\frac {1}{2}}^{\frac {3}{2}}(5 x)+\frac {c_1 (10 x+1)}{10 \sqrt {5} x^{3/2}} \]