Internal problem ID [7346]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 626.
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}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.091 (sec). Leaf size: 44
dsolve(x^2*(1+x^2)*diff(y(x),x$2)+x*(5+2*x^2)*diff(y(x),x)-21*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x^{2}+1\right )^{\frac {5}{2}} \left (x^{2}+8\right )}{x^{7}}+\frac {c_{2} \left (35 x^{6}+140 x^{4}+168 x^{2}+64\right )}{x^{7}} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 54
DSolve[x^2*(1+x^2)*y''[x]+x*(5+2*x^2)*y'[x]-21*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {35 c_1 \left (x^2+1\right )^{5/2} \left (x^2+8\right )-c_2 \left (7 \left (5 \left (x^2+4\right ) x^2+24\right ) x^2+64\right )}{35 x^7} \\ \end{align*}