Internal problem ID [8078]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 602.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 89
dsolve(x^2*(1+x^2)*diff(y(x),x$2)+x*(3+10*x^2)*diff(y(x),x)-(15-14*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{3}}{\left (x^{2}+1\right )^{\frac {5}{2}}}-\frac {c_{2} \left (-3 \,\operatorname {arctanh}\left (\frac {1}{\sqrt {x^{2}+1}}\right ) x^{8}+3 \sqrt {x^{2}+1}\, x^{6}-2 x^{4} \sqrt {x^{2}+1}-24 \sqrt {x^{2}+1}\, x^{2}-16 \sqrt {x^{2}+1}\right )}{128 x^{5} \left (x^{2}+1\right )^{\frac {5}{2}}} \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 75
DSolve[x^2*(1+x^2)*y''[x]+x*(3+10*x^2)*y'[x]-(15-14*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \left (\sqrt {x^2+1} \left (3 x^6-2 x^4-24 x^2-16\right )-3 x^8 \text {arctanh}\left (\sqrt {x^2+1}\right )\right )+128 c_1 x^8}{128 x^5 \left (x^2+1\right )^{5/2}} \]