Internal problem ID [7122]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 396.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x^{4} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+4*x^4*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \left (x^{2}\right )}{x^{2}}+\frac {c_{2} \cos \left (x^{2}\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 41
DSolve[x^2*y''[x]+3*x*y'[x]+4*x^4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4 c_1 e^{-i x^2}-i c_2 e^{i x^2}}{4 x^2} \\ \end{align*}