Internal problem ID [12406]
Book: Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham,
S.R.Otto. Cambridge Univ. Press 2003
Section: Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL
EQUATIONS. Problems page 28
Problem number: Problem 1.11(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y=0} \] With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(x^3*diff(y(x),x$2)+x^2*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 222
AsymptoticDSolveValue[x^3*y''[x]+x^2*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 e^{-\frac {2 i}{\sqrt {x}}} \sqrt [4]{x} \left (\frac {418854310875 i x^{9/2}}{8796093022208}-\frac {57972915 i x^{7/2}}{4294967296}+\frac {59535 i x^{5/2}}{8388608}-\frac {75 i x^{3/2}}{8192}-\frac {30241281245175 x^5}{281474976710656}+\frac {13043905875 x^4}{549755813888}-\frac {2401245 x^3}{268435456}+\frac {3675 x^2}{524288}-\frac {9 x}{512}+\frac {i \sqrt {x}}{16}+1\right )+c_2 e^{\frac {2 i}{\sqrt {x}}} \sqrt [4]{x} \left (-\frac {418854310875 i x^{9/2}}{8796093022208}+\frac {57972915 i x^{7/2}}{4294967296}-\frac {59535 i x^{5/2}}{8388608}+\frac {75 i x^{3/2}}{8192}-\frac {30241281245175 x^5}{281474976710656}+\frac {13043905875 x^4}{549755813888}-\frac {2401245 x^3}{268435456}+\frac {3675 x^2}{524288}-\frac {9 x}{512}-\frac {i \sqrt {x}}{16}+1\right ) \]