Internal problem ID [2416]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.4. page
758
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }+3 y^{\prime } x +y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 44
Order:=6; dsolve(4*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {1}{4}} \left (1-\frac {1}{5} x +\frac {1}{90} x^{2}-\frac {1}{3510} x^{3}+\frac {1}{238680} x^{4}-\frac {1}{25061400} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1-\frac {1}{3} x +\frac {1}{42} x^{2}-\frac {1}{1386} x^{3}+\frac {1}{83160} x^{4}-\frac {1}{7900200} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 85
AsymptoticDSolveValue[4*x^2*y''[x]+3*x*y'[x]+x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [4]{x} \left (-\frac {x^5}{25061400}+\frac {x^4}{238680}-\frac {x^3}{3510}+\frac {x^2}{90}-\frac {x}{5}+1\right )+c_2 \left (-\frac {x^5}{7900200}+\frac {x^4}{83160}-\frac {x^3}{1386}+\frac {x^2}{42}-\frac {x}{3}+1\right ) \]