Internal problem ID [4749]
Book: Advanced Mathemtical 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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}-\cos \relax (x )=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ 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: 0.1 (sec). Leaf size: 34
AsymptoticDSolveValue[y'[x]-y[x]/x==Cos[x],y[x],{x,0,5}]
\[ y(x)\to x \left (-\frac {x^6}{4320}+\frac {x^4}{96}-\frac {x^2}{4}+\log (x)\right )+c_1 x \]