Internal problem ID [1779]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8, Series solutions. Page 195
Problem number: 14.
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^{\prime }+y t=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1, y^{\prime }\relax (0) = 2] \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)+t*y(t)=0,y(0) = -1, D(y)(0) = 2],y(t),type='series',t=0);
\[ y \relax (t ) = -1+2 t -t^{2}+\frac {1}{2} t^{3}-\frac {7}{24} t^{4}+\frac {13}{120} t^{5}+\mathrm {O}\left (t^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 34
AsymptoticDSolveValue[{y''[t]+y'[t]+t*y[t]==0,{y[0]==-1,y'[0]==2}},y[t],{t,0,5}]
\[ y(t)\to \frac {13 t^5}{120}-\frac {7 t^4}{24}+\frac {t^3}{2}-t^2+2 t-1 \]