Internal problem ID [7752]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 265.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {x y^{\prime }}{2}-\frac {3 y x}{4}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 131
dsolve(x^2*(1-4*x)*diff(y(x),x$2)+((1-(3/2))*x-(6-4*(3/2))*x^2)*diff(y(x),x)+(3/2)*(1-(3/2))*x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sqrt {3 x -1}\, \left (\frac {4 \sqrt {\left (-1+4 x \right ) x}\, x +8 x^{2}-2 \sqrt {\left (-1+4 x \right ) x}-5 x +1}{5 x -1+2 \sqrt {\left (-1+4 x \right ) x}}\right )^{\frac {1}{4}}+c_{2} \sqrt {3 x -1}\, \left (\frac {5 x -1+2 \sqrt {\left (-1+4 x \right ) x}}{4 \sqrt {\left (-1+4 x \right ) x}\, x +8 x^{2}-2 \sqrt {\left (-1+4 x \right ) x}-5 x +1}\right )^{\frac {1}{4}} \]
✓ Solution by Mathematica
Time used: 0.385 (sec). Leaf size: 111
DSolve[x^2*(1-4*x)*y''[x]+((1-(3/2))*x-(6-4*(3/2))*x^2)*y'[x]+(3/2)*(1-(3/2))*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt [4]{x} \sqrt [4]{4 x-1} \left (6 c_1 \left (\sqrt {4 x-1}-i\right )^{3/2}+i c_2 \left (\sqrt {4 x-1}+i\right )^{3/2}\right )}{6 \sqrt [4]{1-4 x} \sqrt [4]{\sqrt {4 x-1}-i} \sqrt [4]{\sqrt {4 x-1}+i}} \]