Internal problem ID [4835]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.2 page
239
Problem number: 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime }+\lambda y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(x^4*diff(y(x),x$2)+lambda*y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.167 (sec). Leaf size: 50
AsymptoticDSolveValue[x^4*y''[x]+\[Lambda]*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x e^{\frac {i \sqrt {\lambda }}{x}}-\frac {i c_2 x e^{-\frac {i \sqrt {\lambda }}{x}}}{2 \sqrt {\lambda }} \]