Internal problem ID [7662]
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]]
\[ \boxed {x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 62
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)
\[ y \left (x \right ) = c_{1} \left (x^{5}-\frac {5}{2} x^{4}\right )+c_{2} \left (3 x^{5} \ln \left (x \right )+\frac {x^{6}}{4}-\frac {15 x^{4} \ln \left (x \right )}{2}-\frac {5 x^{5}}{8}-\frac {299 x^{4}}{16}+5 x^{3}+\frac {5 x^{2}}{4}+\frac {x}{4}+\frac {1}{40}\right ) \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 68
DSolve[x^2*(1+x)*y''[x]-x*(3+10*x)*y'[x]+30*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \left (x^5-\frac {5 x^4}{2}\right )+\frac {1}{20} c_2 \left (20 x^6-50 x^5-1495 x^4+120 (2 x-5) x^4 \log (x)+400 x^3+100 x^2+20 x+2\right ) \]