Internal problem ID [1782]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8, Series solutions. Page 195
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-t}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 5] \end {align*}
With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([diff(y(t),t$2)+diff(y(t),t)+exp(-t)*y(t)=0,y(0) = 3, D(y)(0) = 5],y(t),type='series',t=0);
\[ y \left (t \right ) = 3+5 t -4 t^{2}+t^{3}+\frac {3}{8} t^{4}-\frac {17}{40} t^{5}+\operatorname {O}\left (t^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 30
AsymptoticDSolveValue[{y''[t]+y'[t]+Exp[-t]*y[t]==0,{y[0]==3,y'[0]==5}},y[t],{t,0,5}]
\[ y(t)\to -\frac {17 t^5}{40}+\frac {3 t^4}{8}+t^3-4 t^2+5 t+3 \]