Internal problem ID [7344]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 624.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.133 (sec). Leaf size: 43
dsolve(4*x^2*(1+x^2)*diff(y(x),x$2)+8*x*diff(y(x),x)-(35-x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x^{2}+1\right )^{2}}{x^{\frac {7}{2}}}+\frac {c_{2} \left (\left (x^{2}+1\right )^{2} \ln \left (x^{2}+1\right )+2 x^{2}+\frac {3}{2}\right )}{x^{\frac {7}{2}}} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 53
DSolve[4*x^2*(1+x^2)*y''[x]+8*x*y'[x]-(35-x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4 c_1 \left (x^2+1\right )^2+c_2 \left (4 x^2+3\right )+2 c_2 \left (x^2+1\right )^2 \log \left (x^2+1\right )}{4 x^{7/2}} \\ \end{align*}