Internal problem ID [4827]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+2 y^{\prime }-y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 32
Order:=6; dsolve(x*diff(y(x),x$2)+2*diff(y(x),x)-x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \left (1+\frac {1}{6} x^{2}+\frac {1}{120} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (1+\frac {1}{2} x^{2}+\frac {1}{24} x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 42
AsymptoticDSolveValue[x*y''[x]+2*y'[x]-x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^3}{24}+\frac {x}{2}+\frac {1}{x}\right )+c_2 \left (\frac {x^4}{120}+\frac {x^2}{6}+1\right ) \]