Internal problem ID [7287]
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]]
Solve \begin {gather*} \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} \end {gather*}
✓ Solution by Maple
Time used: 0.391 (sec). Leaf size: 123
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)
\[ y \relax (x ) = \frac {c_{1} x^{\frac {1}{6}}}{\left (2 x -1\right )^{\frac {4}{3}}}+c_{2} \left (-\frac {4 x^{\frac {1}{6}} \ln \left (1+\left (2 x -1\right )^{\frac {1}{3}}\right )}{3 \left (2 x -1\right )^{\frac {4}{3}}}+\frac {2 x^{\frac {1}{6}} \ln \left (1-\left (2 x -1\right )^{\frac {1}{3}}+\left (2 x -1\right )^{\frac {2}{3}}\right )}{3 \left (2 x -1\right )^{\frac {4}{3}}}+\frac {4 \sqrt {3}\, x^{\frac {1}{6}} \arctan \left (\frac {\sqrt {3}\, \left (2 x -1\right )^{\frac {1}{3}}}{-2+\left (2 x -1\right )^{\frac {1}{3}}}\right )}{3 \left (2 x -1\right )^{\frac {4}{3}}}+\frac {4 x^{\frac {1}{6}}}{2 x -1}\right ) \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 108
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]
\begin{align*} y(x)\to \frac {\sqrt [6]{x} \left (-c_2 \left (2 \sqrt {3} \text {ArcTan}\left (\frac {2 \sqrt [3]{1-2 x}+1}{\sqrt {3}}\right )-2 \log \left (\sqrt [3]{1-2 x}-1\right )+\log \left ((1-2 x)^{2/3}+\sqrt [3]{1-2 x}+1\right )\right )+6 c_2 \sqrt [3]{1-2 x}+2 c_1\right )}{2 (1-2 x)^{4/3}} \\ \end{align*}