Internal problem ID [747]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 5.3, Series Solutions Near an Ordinary Point, Part II. page 269
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 21
Order:=6; dsolve(diff(y(x),x)-x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{2} x^{2}+\frac {1}{8} x^{4}\right ) y \relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 22
AsymptoticDSolveValue[y'[x]-x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^4}{8}+\frac {x^2}{2}+1\right ) \]