45.4.6 problem 14

Internal problem ID [7288]
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. Chapter 6 review exercises. page 253
Problem number : 14
Date solved : Monday, January 27, 2025 at 02:49:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

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

\[ y = \left (-\frac {x^{2}}{2}+1\right ) y \left (0\right )+\left (x -\frac {1}{6} x^{3}-\frac {1}{60} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 35

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

\[ y(x)\to c_1 \left (1-\frac {x^2}{2}\right )+c_2 \left (-\frac {x^5}{60}-\frac {x^3}{6}+x\right ) \]