Internal problem ID [4748]
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 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-2 y^{\prime }+y-\cos \relax (x )=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=6; dsolve(x*diff(y(x),x$2)-2*diff(y(x),x)+y(x)=cos(x),y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.268 (sec). Leaf size: 312
AsymptoticDSolveValue[x*y''[x]-2*y'[x]+y[x]==Cos[x],y[x],{x,0,5}]
\[ y(x)\to c_1 \left (x^4 \left (\frac {\log (x)}{48}-\frac {5}{192}\right )-\frac {1}{12} x^3 \log (x)+\frac {x^2}{4}+\frac {x}{2}+1\right )+c_2 \left (-\frac {x^5}{806400}+\frac {x^4}{20160}-\frac {x^3}{720}+\frac {x^2}{40}-\frac {x}{4}+1\right ) x^3+\left (-\frac {x^5}{806400}+\frac {x^4}{20160}-\frac {x^3}{720}+\frac {x^2}{40}-\frac {x}{4}+1\right ) x^3 \left (\frac {x^6 \left (-20160 \log ^2(x)+141222 \log (x)-201569\right )}{3135283200}+\frac {x^5 (22277-114360 \log (x))}{435456000}+\frac {x^4 (69541-29064 \log (x))}{34836480}+\frac {x^3 (1860 \log (x)+193)}{388800}-\frac {1}{6 x^2}+\frac {x^2 (4 \log (x)-23)}{1152}-\frac {1}{6 x}+\frac {1}{36} x (-\log (x)-2)-\frac {\log (x)}{12}\right )+\left (\frac {x^6 (5791-672 \log (x))}{8709120}-\frac {589 x^5}{302400}-\frac {89 x^4}{8640}+\frac {19 x^3}{360}+\frac {x^2}{24}-\frac {x}{3}\right ) \left (x^4 \left (\frac {\log (x)}{48}-\frac {5}{192}\right )-\frac {1}{12} x^3 \log (x)+\frac {x^2}{4}+\frac {x}{2}+1\right ) \]