Internal problem ID [1803]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {4 t y^{\prime \prime }+3 y^{\prime }-3 y=0} \end {gather*} With the expansion point for the power series method at \(t = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
Order:=6; dsolve(4*t*diff(y(t),t$2)+3*diff(y(t),t)-3*y(t)=0,y(t),type='series',t=0);
\[ y \relax (t ) = c_{1} t^{\frac {1}{4}} \left (1+\frac {3}{5} t +\frac {1}{10} t^{2}+\frac {1}{130} t^{3}+\frac {3}{8840} t^{4}+\frac {3}{309400} t^{5}+\mathrm {O}\left (t^{6}\right )\right )+c_{2} \left (1+t +\frac {3}{14} t^{2}+\frac {3}{154} t^{3}+\frac {3}{3080} t^{4}+\frac {9}{292600} t^{5}+\mathrm {O}\left (t^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 81
AsymptoticDSolveValue[4*t*y''[t]+3*y'[t]-3*y[t]==0,y[t],{t,0,5}]
\[ y(t)\to c_1 \sqrt [4]{t} \left (\frac {3 t^5}{309400}+\frac {3 t^4}{8840}+\frac {t^3}{130}+\frac {t^2}{10}+\frac {3 t}{5}+1\right )+c_2 \left (\frac {9 t^5}{292600}+\frac {3 t^4}{3080}+\frac {3 t^3}{154}+\frac {3 t^2}{14}+t+1\right ) \]