Internal problem ID [11056]
Book: Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto.
Cambridge Univ. Press 2003
Section: Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL EQUATIONS.
Problems page 28
Problem number: Problem 1.8(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }+4 y^{\prime }-x y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
Order:=6; dsolve(x*diff(y(x),x$2)+4*diff(y(x),x)-x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} \left (1+\frac {1}{10} x^{2}+\frac {1}{280} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (12-6 x^{2}-\frac {3}{2} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 42
AsymptoticDSolveValue[x*y''[x]+4*y'[x]-x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{x^3}-\frac {x}{8}-\frac {1}{2 x}\right )+c_2 \left (\frac {x^4}{280}+\frac {x^2}{10}+1\right ) \]