Internal problem ID [5823]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. Section 6.2 SOLUTIONS
ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number: 25 expansion at 0.
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^{\prime }+5 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 69
Order:=8; dsolve(cos(x)*diff(y(x),x$2)+diff(y(x),x)+5*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {5}{2} x^{2}+\frac {5}{6} x^{3}+\frac {5}{8} x^{4}-\frac {5}{24} x^{5}+\frac {1}{16} x^{6}-\frac {13}{336} x^{7}\right ) y \relax (0)+\left (x -\frac {1}{2} x^{2}-\frac {2}{3} x^{3}+\frac {1}{3} x^{4}+\frac {1}{80} x^{6}+\frac {11}{5040} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 91
AsymptoticDSolveValue[Cos[x]*y''[x]+y'[x]+5*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {11 x^7}{5040}+\frac {x^6}{80}+\frac {x^4}{3}-\frac {2 x^3}{3}-\frac {x^2}{2}+x\right )+c_1 \left (-\frac {13 x^7}{336}+\frac {x^6}{16}-\frac {5 x^5}{24}+\frac {5 x^4}{8}+\frac {5 x^3}{6}-\frac {5 x^2}{2}+1\right ) \]