42.1.19 problem 3.48 (a)

Internal problem ID [6841]
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 : 3.48 (a)
Date solved : Monday, January 27, 2025 at 02:31:31 PM
CAS classification : [_linear]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 35

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

\[ y = \left (1-\frac {1}{2} x^{2}+\frac {1}{8} x^{4}\right ) y \left (0\right )+x -\frac {x^{3}}{2}+\frac {13 x^{5}}{120}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 38

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

\[ y(x)\to \frac {13 x^5}{120}-\frac {x^3}{2}+c_1 \left (\frac {x^4}{8}-\frac {x^2}{2}+1\right )+x \]