46.1.3 problem 8

Internal problem ID [7293]
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
Date solved : Monday, January 27, 2025 at 02:49:49 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }-3 y&=k \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 24

Order:=6; 
dsolve(x*diff(y(x),x)-3*y(x)=k,y(x),type='series',x=0);
 

\[ y = c_{1} x^{3} \left (1+\operatorname {O}\left (x^{6}\right )\right )+\left (-\frac {k}{3}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 15

AsymptoticDSolveValue[x*D[y[x],x]-3*y[x]==k,y[x],{x,0,"6"-1}]
 

\[ y(x)\to -\frac {k}{3}+c_1 x^3 \]