73.24.23 problem 34.8 b(iii)

Internal problem ID [15703]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 34. Power series solutions II: Generalization and theory. Additional Exercises. page 678
Problem number : 34.8 b(iii)
Date solved : Tuesday, January 28, 2025 at 08:05:37 AM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 47

Order:=8; 
dsolve(cos(x)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-x +\frac {1}{2} x^{2}-\frac {1}{3} x^{3}+\frac {5}{24} x^{4}-\frac {2}{15} x^{5}+\frac {61}{720} x^{6}-\frac {17}{315} x^{7}\right ) y \left (0\right )+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 53

AsymptoticDSolveValue[Cos[x]*D[y[x],x]+y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_1 \left (-\frac {17 x^7}{315}+\frac {61 x^6}{720}-\frac {2 x^5}{15}+\frac {5 x^4}{24}-\frac {x^3}{3}+\frac {x^2}{2}-x+1\right ) \]