Internal problem ID [6528]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 57.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}+3 y^{\prime } x +4 x^{4} y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 28
Order:=6; dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+4*x^4*y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \left (1-\frac {1}{6} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (-2+x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 30
AsymptoticDSolveValue[x^2*y''[x]+3*x*y'[x]+4*x^4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (1-\frac {x^4}{6}\right )+c_1 \left (\frac {1}{x^2}-\frac {x^2}{2}\right ) \]