Internal problem ID [4523]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{\prime }+\sin \relax (t ) x=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 1] \end {align*}
With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
Order:=6; dsolve([diff(x(t),t)+sin(t)*x(t)=0,x(0) = 1],x(t),type='series',t=0);
\[ x \relax (t ) = 1-\frac {1}{2} t^{2}+\frac {1}{6} t^{4}+\mathrm {O}\left (t^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 19
AsymptoticDSolveValue[{x'[t]+Sin[t]*x[t]==0,{x[0]==1}},x[t],{t,0,5}]
\[ x(t)\to \frac {t^4}{6}-\frac {t^2}{2}+1 \]