42.1.23 problem 3.50

Internal problem ID [6845]
Book : Advanced Mathematical Methods for Scientists and Engineers, Bender and Orszag. Springer October 29, 1999
Section : Chapter 3. APPROXIMATE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS. page 136
Problem number : 3.50
Date solved : Monday, January 27, 2025 at 02:31:36 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {y}{x}&=\cos \left (x \right ) \end{align*}

Using series method with expansion around

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

✗ Solution by Maple

Order:=6; 
dsolve(diff(y(x),x)-y(x)/x=cos(x),y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 34

AsymptoticDSolveValue[D[y[x],x]-y[x]/x==Cos[x],y[x],{x,0,"6"-1}]
 

\[ y(x)\to x \left (-\frac {x^6}{4320}+\frac {x^4}{96}-\frac {x^2}{4}+\log (x)\right )+c_1 x \]