Internal problem ID [7588]
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]]
\[ \boxed {x^{2} \left (2+x \right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (-8 x +2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 116
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)
\[ y \left (x \right ) = \frac {c_{1} \left (40 x^{4}-160 x^{3}+60 x^{2}+8 x +1\right )}{x^{2}}+\frac {c_{2} \left (x^{\frac {3}{2}} \left (40 x^{4}-160 x^{3}+60 x^{2}+8 x +1\right ) \operatorname {arcsinh}\left (\frac {\sqrt {x}\, \sqrt {2}}{2}\right )+\frac {\sqrt {x +2}\, x^{2} \left (8 x^{5}+328 x^{4}-13974 x^{3}+26734 x^{2}-805 x -105\right )}{210}\right ) \left (-2-x \right )^{\frac {3}{4}}}{\left (x +2\right )^{\frac {3}{4}} x^{\frac {7}{2}}} \]
✓ Solution by Mathematica
Time used: 48.622 (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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