Internal problem ID [4900]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.3. Extended Power
Series Method: Frobenius Method page 186
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 t \left (t +1\right ) y^{\prime \prime }+y^{\prime } t -y=0} \end {gather*} With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 42
Order:=6; dsolve(3*t*(1+t)*diff(y(t),t$2)+t*diff(y(t),t)-y(t)=0,y(t),type='series',t=0);
\[ y \relax (t ) = c_{1} t \left (1+\mathrm {O}\left (t^{6}\right )\right )+\left (\frac {1}{3} t +\mathrm {O}\left (t^{6}\right )\right ) \ln \relax (t ) c_{2}+\left (1-\frac {1}{3} t -\frac {2}{9} t^{2}+\frac {7}{81} t^{3}-\frac {35}{729} t^{4}+\frac {91}{2916} t^{5}+\mathrm {O}\left (t^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 43
AsymptoticDSolveValue[3*t*(1+t)*y''[t]+t*y'[t]-y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_1 \left (\frac {1}{729} \left (-35 t^4+63 t^3-162 t^2+243 t+729\right )+\frac {1}{3} t \log (t)\right )+c_2 t \]