Internal problem ID [5830]
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: 30 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y \cos \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 24
Order:=8; dsolve([diff(y(x),x$2)+cos(x)*y(x)=0,y(0) = 1, D(y)(0) = 1],y(x),type='series',x=0);
\[ y \relax (x ) = 1+x -\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{12} x^{4}+\frac {1}{30} x^{5}-\frac {1}{80} x^{6}-\frac {19}{5040} x^{7}+\mathrm {O}\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 48
AsymptoticDSolveValue[{y''[x]+Cos[x]*y[x]==0,{y[0]==1,y'[0]==1}},y[x],{x,0,7}]
\[ y(x)\to -\frac {19 x^7}{5040}-\frac {x^6}{80}+\frac {x^5}{30}+\frac {x^4}{12}-\frac {x^3}{6}-\frac {x^2}{2}+x+1 \]