Internal problem ID [4899]
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: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y=0} \end {gather*} With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
Order:=6; dsolve(2*(t^2-5*t+6)*diff(y(t),t$2)+(2*t-3)*diff(y(t),t)-8*y(t)=0,y(t),type='series',t=0);
\[ y \relax (t ) = \left (1+\frac {1}{3} t^{2}+\frac {13}{108} t^{3}+\frac {299}{5184} t^{4}+\frac {923}{34560} t^{5}\right ) y \relax (0)+\left (t +\frac {1}{8} t^{2}+\frac {37}{288} t^{3}+\frac {851}{13824} t^{4}+\frac {2627}{92160} t^{5}\right ) D\relax (y )\relax (0)+O\left (t^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 70
AsymptoticDSolveValue[2*(t^2-5*t+6)*y''[t]+(2*t-3)*y'[t]-8*y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_1 \left (\frac {923 t^5}{34560}+\frac {299 t^4}{5184}+\frac {13 t^3}{108}+\frac {t^2}{3}+1\right )+c_2 \left (\frac {2627 t^5}{92160}+\frac {851 t^4}{13824}+\frac {37 t^3}{288}+\frac {t^2}{8}+t\right ) \]