Internal problem ID [5625]
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]
\[ \boxed {x y^{\prime }-3 y=k} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
Order:=6; dsolve(x*diff(y(x),x)-3*y(x)=k,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{3} \left (1+\operatorname {O}\left (x^{6}\right )\right )+\left (-\frac {k}{3}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 15
AsymptoticDSolveValue[x*y'[x]-3*y[x]==k,y[x],{x,0,5}]
\[ y(x)\to -\frac {k}{3}+c_1 x^3 \]