Internal problem ID [1772]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8, Series solutions. Page 195
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4 t +4\right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 0, y^{\prime }\left (-1\right ) = 1] \end {align*}
With the expansion point for the power series method at \(t = -1\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 12
Order:=6; dsolve([diff(y(t),t$2)+(t^2+2*t+1)*diff(y(t),t)-(4+4*t)*y(t)=0,y(-1) = 0, D(y)(-1) = 1],y(t),type='series',t=-1);
\[ y \relax (t ) = \left (t +1\right )+\frac {1}{4} \left (t +1\right )^{4}+\mathrm {O}\left (\left (t +1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 15
AsymptoticDSolveValue[{y''[t]+(t^2+2*t+1)*y'[t]-(4+4*t)*y[t]==0,{y[-1]==0,y'[-1]==1}},y[t],{t,-1,5}]
\[ y(t)\to \frac {1}{4} (t+1)^4+t+1 \]