45.2.33 problem 33

Internal problem ID [7256]
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
Date solved : Monday, January 27, 2025 at 02:49:07 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{4} y^{\prime \prime }+\lambda y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✗ 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: 0.124 (sec). Leaf size: 54

AsymptoticDSolveValue[x^4*D[y[x],{x,2}]+\[Lambda]*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 x e^{-1+\frac {i \sqrt {\lambda }}{x}}-\frac {i c_2 x e^{1-\frac {i \sqrt {\lambda }}{x}}}{2 \sqrt {\lambda }} \]