46.5.1 problem 11

Internal problem ID [7337]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 5. Series Solutions of ODEs. REVIEW QUESTIONS. page 201
Problem number : 11
Date solved : Monday, January 27, 2025 at 02:50:38 PM
CAS classification : [[_2nd_order, _missing_x]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

Order:=6; 
dsolve(diff(y(x),x$2)+4*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-2 x^{2}+\frac {2}{3} x^{4}\right ) y \left (0\right )+\left (x -\frac {2}{3} x^{3}+\frac {2}{15} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 40

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

\[ y(x)\to c_2 \left (\frac {2 x^5}{15}-\frac {2 x^3}{3}+x\right )+c_1 \left (\frac {2 x^4}{3}-2 x^2+1\right ) \]