Internal problem ID [6835]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 103.
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}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(x*(3+x^2)*diff(y(x),x$2)+(2-x^2)*diff(y(x),x)-8*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{\frac {1}{3}} \left (x^{2}+3\right )^{\frac {11}{6}}+c_{2} \left (x^{4}+\frac {11}{2} x^{2}+\frac {55}{8}\right ) \]
✓ Solution by Mathematica
Time used: 1.09 (sec). Leaf size: 41
DSolve[x*(3+x^2)*y''[x]+(2-x^2)*y'[x]-8*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \sqrt [3]{x} \left (x^2+3\right )^{11/6}-\frac {1}{55} c_2 \left (8 x^4+44 x^2+55\right ) \\ \end{align*}