Internal problem ID [7263]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 543.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 43
dsolve(x*(1+x^2)*diff(y(x),x$2)+(4+7*x^2)*diff(y(x),x)+8*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\sqrt {x^{2}+1}\, x^{3}}+\frac {c_{2} \left (x \sqrt {x^{2}+1}-\arcsinh \relax (x )\right )}{\sqrt {x^{2}+1}\, x^{3}} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 55
DSolve[x*(1+x^2)*y''[x]+(4+7*x^2)*y'[x]+8*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x \sqrt {x^2+1}-c_2 \tanh ^{-1}\left (\frac {x}{\sqrt {x^2+1}}\right )+2 c_1}{2 x^3 \sqrt {x^2+1}} \\ \end{align*}