Internal problem ID [2419]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.4. page
758
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }+y^{\prime }-2 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 32
Order:=6; dsolve(2*x*diff(y(x),x$2)+diff(y(x),x)-2*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} \sqrt {x}\, \left (1+\frac {1}{5} x^{2}+\frac {1}{90} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1+\frac {1}{3} x^{2}+\frac {1}{42} x^{4}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 47
AsymptoticDSolveValue[2*x*y''[x]+y'[x]-2*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt {x} \left (\frac {x^4}{90}+\frac {x^2}{5}+1\right )+c_2 \left (\frac {x^4}{42}+\frac {x^2}{3}+1\right ) \]