Internal problem ID [4867]
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.
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=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)+y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (-\frac {x^{2}}{2}+1\right ) y \relax (0)+\left (x -\frac {1}{6} x^{3}-\frac {1}{60} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 35
AsymptoticDSolveValue[Cos[x]*y''[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (1-\frac {x^2}{2}\right )+c_2 \left (-\frac {x^5}{60}-\frac {x^3}{6}+x\right ) \]