Internal problem ID [4527]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-{\mathrm e}^{2 x} y^{\prime }+y \cos \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1, y^{\prime }\relax (0) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([diff(y(x),x$2)-exp(2*x)*diff(y(x),x)+cos(x)*y(x)=0,y(0) = -1, D(y)(0) = 1],y(x),type='series',x=0);
\[ y \relax (x ) = -1+x +x^{2}+\frac {1}{2} x^{3}+\frac {1}{2} x^{4}+\frac {31}{60} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 30
AsymptoticDSolveValue[{y''[x]-Exp[2*x]*y'[x]+Cos[x]*y[x]==0,{y[0]==-1,y'[0]==1}},y[x],{x,0,5}]
\[ y(x)\to \frac {31 x^5}{60}+\frac {x^4}{2}+\frac {x^3}{2}+x^2+x-1 \]