Internal problem ID [1797]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8.2, Regular singular points, the method of Frobenius. Page 214
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y=0} \end {gather*} With the expansion point for the power series method at \(t = -1\).
✗ Solution by Maple
Order:=6; dsolve((1-t^2)*diff(y(t),t$2)+1/sin(t+1)*diff(y(t),t)+y(t)=0,y(t),type='series',t=-1);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 111
AsymptoticDSolveValue[(1-t^2)*y''[t]+1/Sin[t+1]*y'[t]+y[t]==0,y[t],{t,-1,5}]
\[ y(t)\to c_2 e^{\frac {1}{2 (t+1)}} \left (\frac {516353141702117 (t+1)^5}{33443020800}+\frac {53349163853 (t+1)^4}{39813120}+\frac {58276991 (t+1)^3}{414720}+\frac {21397 (t+1)^2}{1152}+\frac {79 (t+1)}{24}+1\right ) (t+1)^{7/4}+c_1 \left (\frac {53}{5} (t+1)^5-\frac {25}{12} (t+1)^4+\frac {2}{3} (t+1)^3-\frac {1}{2} (t+1)^2+1\right ) \]