Internal problem ID [4745]
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: 3.48 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x y+y^{\prime }-\cos \relax (x )=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
Order:=6; dsolve(diff(y(x),x)+x*y(x)=cos(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{2} x^{2}+\frac {1}{8} x^{4}\right ) y \relax (0)+x -\frac {x^{3}}{2}+\frac {13 x^{5}}{120}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 38
AsymptoticDSolveValue[y'[x]+x*y[x]==Cos[x],y[x],{x,0,5}]
\[ y(x)\to \frac {13 x^5}{120}-\frac {x^3}{2}+c_1 \left (\frac {x^4}{8}-\frac {x^2}{2}+1\right )+x \]