Internal problem ID [6906]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 174.
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 +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 64
dsolve(x^2*(1+x)*diff(y(x),x$2)-x*(3+10*x)*diff(y(x),x)+30*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (2 x^{5}-5 x^{4}\right )+c_{2} \left (\left (3 x^{5}-\frac {15}{2} x^{4}\right ) \ln \relax (x )+\frac {x^{6}}{4}-\frac {5 x^{5}}{8}-\frac {299 x^{4}}{16}+5 x^{3}+\frac {5 x^{2}}{4}+\frac {x}{4}+\frac {1}{40}\right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 67
DSolve[x^2*(1+x)*y''[x]-x*(3+10*x)*y'[x]+30*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} c_1 (2 x-5) x^4+6 c_2 (2 x-5) x^4 \log (x)+\frac {1}{20} c_2 (5 x (x (x (x (2 x (2 x-5)-299)+80)+20)+4)+2) \\ \end{align*}