Internal problem ID [7310]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 590.
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 (-x^{2}+1\right ) y^{\prime }-8 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 48
dsolve(x*(1+x^2)*diff(y(x),x$2)+(1-x^2)*diff(y(x),x)-8*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x^{2}+1\right )^{2}+c_{2} \left (-\frac {\left (x^{2}+1\right )^{2} \ln \left (x^{2}+1\right )}{2}+\left (x^{2}+1\right )^{2} \ln \relax (x )+\frac {x^{2}}{2}+\frac {3}{4}\right ) \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 55
DSolve[x*(1+x^2)*y''[x]+(1-x^2)*y'[x]-8*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x^2+1\right )^2+\frac {1}{4} c_2 \left (2 x^2+4 \left (x^2+1\right )^2 \log (x)-2 \left (x^2+1\right )^2 \log \left (x^2+1\right )+3\right ) \\ \end{align*}