Internal problem ID [6527]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 56.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime } x^{2}+5 y^{\prime } x +4 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 41
Order:=6; dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+4*y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = x^{-\frac {3}{4}-\frac {i \sqrt {23}}{4}} c_{1}+x^{-\frac {3}{4}+\frac {i \sqrt {23}}{4}} c_{2}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 44
AsymptoticDSolveValue[2*x^2*y''[x]+5*x*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x^{\frac {1}{4} \left (-3+i \sqrt {23}\right )}+c_2 x^{\frac {1}{4} \left (-3-i \sqrt {23}\right )} \]