Internal problem ID [5297]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 4. Linear equations with Regular Singular Points. Page 159
Problem number: 1(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {3 x^{2} y^{\prime \prime }+5 x y^{\prime }+3 x y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 52
Order:=8; dsolve(3*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+3*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} \left (1-\frac {3}{5} x +\frac {9}{80} x^{2}-\frac {9}{880} x^{3}+\frac {27}{49280} x^{4}-\frac {81}{4188800} x^{5}+\frac {81}{167552000} x^{6}-\frac {243}{26975872000} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) x^{\frac {2}{3}}+c_{1} \left (1-3 x +\frac {9}{8} x^{2}-\frac {9}{56} x^{3}+\frac {27}{2240} x^{4}-\frac {81}{145600} x^{5}+\frac {81}{4659200} x^{6}-\frac {243}{619673600} x^{7}+\mathrm {O}\left (x^{8}\right )\right )}{x^{\frac {2}{3}}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 111
AsymptoticDSolveValue[3*x^2*y''[x]+5*x*y'[x]+3*x*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (-\frac {243 x^7}{26975872000}+\frac {81 x^6}{167552000}-\frac {81 x^5}{4188800}+\frac {27 x^4}{49280}-\frac {9 x^3}{880}+\frac {9 x^2}{80}-\frac {3 x}{5}+1\right )+\frac {c_2 \left (-\frac {243 x^7}{619673600}+\frac {81 x^6}{4659200}-\frac {81 x^5}{145600}+\frac {27 x^4}{2240}-\frac {9 x^3}{56}+\frac {9 x^2}{8}-3 x+1\right )}{x^{2/3}} \]