43.2.15 problem 7.3.101 (e)

Internal problem ID [6872]
Book : Notes on Diffy Qs. Differential Equations for Engineers. By by Jiri Lebl, 2013.
Section : Chapter 7. POWER SERIES METHODS. 7.3.2 The method of Frobenius. Exercises. page 300
Problem number : 7.3.101 (e)
Date solved : Monday, January 27, 2025 at 02:32:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \cos \left (x \right ) y^{\prime \prime }-y \sin \left (x \right )&=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)-sin(x)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1+\frac {1}{6} x^{3}+\frac {1}{60} x^{5}\right ) y \left (0\right )+\left (x +\frac {1}{12} x^{4}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

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

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

\[ y(x)\to c_2 \left (\frac {x^4}{12}+x\right )+c_1 \left (\frac {x^5}{60}+\frac {x^3}{6}+1\right ) \]