Internal problem ID [4872]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.1. page
174
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y^{\prime }-3 y-k=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 24
Order:=6; dsolve(x*diff(y(x),x)-3*y(x)=k,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{3} \left (1+\mathrm {O}\left (x^{6}\right )\right )+\left (-\frac {k}{3}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 15
AsymptoticDSolveValue[x*y'[x]-3*y[x]==k,y[x],{x,0,5}]
\[ y(x)\to -\frac {k}{3}+c_1 x^3 \]