Internal problem ID [6872]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 140.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +7\right ) y^{\prime }+\left (9-x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 71
dsolve(x^2*(1-x)*diff(y(x),x$2)+x*(7+x)*diff(y(x),x)+(9-x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x^{4}+16 x^{3}+36 x^{2}+16 x +1\right )}{x^{3}}+\frac {c_{2} \left (\left (3 x^{4}+48 x^{3}+108 x^{2}+48 x +3\right ) \ln \relax (x )+120 x^{3}+450 x^{2}+280 x +25\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 70
DSolve[x^2*(1-x)*y''[x]+x*(7+x)*y'[x]+(9-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 c_1 (x (x+2) (x (x+14)+8)+1)+5 c_2 (2 x (3 x (4 x+15)+28)+5)+3 c_2 (x (x+2) (x (x+14)+8)+1) \log (x)}{3 x^3} \\ \end{align*}