Internal problem ID [1769]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8, Series solutions. Page 195
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {t \left (2-t \right ) y^{\prime \prime }-6 \left (t -1\right ) y^{\prime }-4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = 0] \end {align*}
With the expansion point for the power series method at \(t = 1\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 14
Order:=6; dsolve([t*(2-t)*diff(y(t),t$2)-6*(t-1)*diff(y(t),t)-4*y(t)=0,y(1) = 1, D(y)(1) = 0],y(t),type='series',t=1);
\[ y \relax (t ) = 1+2 \left (t -1\right )^{2}+3 \left (t -1\right )^{4}+\mathrm {O}\left (\left (t -1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 19
AsymptoticDSolveValue[{t*(2-t)*y''[t]-6*(t-1)*y'[t]-4*y[t]==0,{y[1]==1,y'[1]==0}},y[t],{t,1,5}]
\[ y(t)\to 3 (t-1)^4+2 (t-1)^2+1 \]