Internal problem ID [4833]
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: 31.
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 }+\left (x -6\right ) y^{\prime }-3 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 40
Order:=6; dsolve(x*diff(y(x),x$2)+(x-6)*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{7} \left (1-\frac {1}{2} x +\frac {5}{36} x^{2}-\frac {1}{36} x^{3}+\frac {7}{1584} x^{4}-\frac {7}{11880} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (3628800-1814400 x +362880 x^{2}-30240 x^{3}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 63
AsymptoticDSolveValue[x*y''[x]+(x-6)*y'[x]-3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^3}{120}+\frac {x^2}{10}-\frac {x}{2}+1\right )+c_2 \left (\frac {7 x^{11}}{1584}-\frac {x^{10}}{36}+\frac {5 x^9}{36}-\frac {x^8}{2}+x^7\right ) \]