Internal problem ID [8043]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 567.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(36*x^2*(1-2*x)*diff(y(x),x$2)+24*x*(1-9*x)*diff(y(x),x)+(1-70*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{\frac {1}{6}}}{\left (-1+2 x \right )^{\frac {4}{3}}}+\frac {c_{2} x^{\frac {1}{6}} \left (\int \frac {\left (-1+2 x \right )^{\frac {1}{3}}}{x}d x \right )}{\left (-1+2 x \right )^{\frac {4}{3}}} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 111
DSolve[36*x^2*(1-2*x)*y''[x]+24*x*(1-9*x)*y'[x]+(1-70*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt [6]{x} \left (-2 \sqrt {3} c_2 \arctan \left (\frac {2 \sqrt [3]{1-2 x}+1}{\sqrt {3}}\right )+6 c_2 \sqrt [3]{1-2 x}+2 c_2 \log \left (\sqrt [3]{1-2 x}-1\right )-c_2 \log \left ((1-2 x)^{2/3}+\sqrt [3]{1-2 x}+1\right )+2 c_1\right )}{2 (1-2 x)^{4/3}} \]