Internal problem ID [4776]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\cos \relax (x ) y^{\prime \prime }-y \sin \relax (x )=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 29
Order:=6; dsolve(cos(x)*diff(y(x),x$2)-sin(x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{6} x^{3}+\frac {1}{60} x^{5}\right ) y \relax (0)+\left (x +\frac {1}{12} x^{4}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 35
AsymptoticDSolveValue[Cos[x]*y''[x]-Sin[x]*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^4}{12}+x\right )+c_1 \left (\frac {x^5}{60}+\frac {x^3}{6}+1\right ) \]