Internal problem ID [6845]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 114.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 43
dsolve(4*x^2*(1+x^2)*diff(y(x),x$2)+4*x*(1+6*x^2)*diff(y(x),x)-(1-25*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \sqrt {x}}{\left (x^{2}+1\right )^{\frac {3}{2}}}+\frac {c_{2} \left (\operatorname {arcsinh}\left (x \right ) x -\sqrt {x^{2}+1}\right )}{\sqrt {x}\, \left (x^{2}+1\right )^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 44
DSolve[4*x^2*(1+x^2)*y''[x]+4*x*(1+6*x^2)*y'[x]-(1-25*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x \text {arcsinh}(x)-c_2 \sqrt {x^2+1}+c_1 x}{\sqrt {x} \left (x^2+1\right )^{3/2}} \\ \end{align*}