Internal problem ID [6720]
Book: Second order enumerated odes
Section: section 2
Problem number: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 41
dsolve(4*x^2*diff(y(x),x$2)+4*x^5*diff(y(x),x)+(x^8+6*x^4+4)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{\frac {1}{2}+\frac {i \sqrt {3}}{2}} {\mathrm e}^{-\frac {x^{4}}{8}}+c_{2} x^{\frac {1}{2}-\frac {i \sqrt {3}}{2}} {\mathrm e}^{-\frac {x^{4}}{8}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 62
DSolve[4*x^2*y''[x]+4*x^5*y'[x]+(x^8+6*x^4+4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^{-\frac {x^4}{8}} x^{\frac {1}{2}-\frac {i \sqrt {3}}{2}} \left (3 c_1-i \sqrt {3} c_2 x^{i \sqrt {3}}\right ) \\ \end{align*}