Internal problem ID [13650]
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: 34.9 b(ii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\cos \left (x \right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 54
Order:=10; dsolve(diff(y(x),x$2)+cos(x)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {1}{2} x^{2}+\frac {1}{12} x^{4}-\frac {1}{80} x^{6}+\frac {11}{8064} x^{8}\right ) y \left (0\right )+\left (x -\frac {1}{6} x^{3}+\frac {1}{30} x^{5}-\frac {19}{5040} x^{7}+\frac {29}{72576} x^{9}\right ) D\left (y \right )\left (0\right )+O\left (x^{10}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 70
AsymptoticDSolveValue[y''[x]+Cos[x]*y[x]==0,y[x],{x,0,9}]
\[ y(x)\to c_2 \left (\frac {29 x^9}{72576}-\frac {19 x^7}{5040}+\frac {x^5}{30}-\frac {x^3}{6}+x\right )+c_1 \left (\frac {11 x^8}{8064}-\frac {x^6}{80}+\frac {x^4}{12}-\frac {x^2}{2}+1\right ) \]