Internal problem ID [6832]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 100.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.344 (sec). Leaf size: 131
dsolve(x^2*(2+x)*diff(y(x),x$2)+5*x*(1-x)*diff(y(x),x)-(2-8*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (40 x^{4}-160 x^{3}+60 x^{2}+8 x +1\right )}{x^{2}}+c_{2} \left (\frac {420 \left (40 x^{4}-160 x^{3}+60 x^{2}+8 x +1\right ) \sqrt {2}\, \left (x +2\right )^{\frac {31}{4}} \left (-x -2\right )^{\frac {3}{4}} \arcsinh \left (\frac {\sqrt {2}\, \sqrt {x}}{2}\right )}{\left (2 x +4\right )^{\frac {17}{2}} x^{2}}+\frac {\left (8 x^{5}+328 x^{4}-13974 x^{3}+26734 x^{2}-805 x -105\right ) \left (-x -2\right )^{\frac {3}{4}}}{128 \left (x +2\right )^{\frac {1}{4}} x^{\frac {3}{2}}}\right ) \]
✓ Solution by Mathematica
Time used: 33.016 (sec). Leaf size: 1347
DSolve[x^2*(2+x)*y''[x]+5*x*(1-x)*y'[x]-(2-8*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
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