Internal problem ID [4816]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.2 page
239
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+y^{\prime }+10 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 59
Order:=6; dsolve(x*diff(y(x),x$2)+diff(y(x),x)+10*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\ln \relax (x ) c_{2}+c_{1}\right ) \left (1-10 x +25 x^{2}-\frac {250}{9} x^{3}+\frac {625}{36} x^{4}-\frac {125}{18} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (20 x -75 x^{2}+\frac {2750}{27} x^{3}-\frac {15625}{216} x^{4}+\frac {3425}{108} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 105
AsymptoticDSolveValue[x*y''[x]+y'[x]+10*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {125 x^5}{18}+\frac {625 x^4}{36}-\frac {250 x^3}{9}+25 x^2-10 x+1\right )+c_2 \left (\frac {3425 x^5}{108}-\frac {15625 x^4}{216}+\frac {2750 x^3}{27}-75 x^2+\left (-\frac {125 x^5}{18}+\frac {625 x^4}{36}-\frac {250 x^3}{9}+25 x^2-10 x+1\right ) \log (x)+20 x\right ) \]