Internal problem ID [4849]
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. 6.3.1 page
250
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+3 y^{\prime }+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: 46
Order:=6; dsolve(x*diff(y(x),x$2)+3*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{2} \left (1-\frac {1}{8} x^{2}+\frac {1}{192} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \relax (x ) \left (x^{2}-\frac {1}{8} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\left (-2+\frac {3}{32} x^{4}+\mathrm {O}\left (x^{6}\right )\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 57
AsymptoticDSolveValue[x*y''[x]+3*y'[x]+x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^4}{192}-\frac {x^2}{8}+1\right )+c_1 \left (\frac {1}{16} \left (x^2-8\right ) \log (x)-\frac {5 x^4-16 x^2-64}{64 x^2}\right ) \]