Internal problem ID [4734]
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: 3.24 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left ({\mathrm e}^{x}-1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 39
Order:=6; dsolve(diff(y(x),x$2)+(exp(x)-1)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{6} x^{3}-\frac {1}{24} x^{4}-\frac {1}{120} x^{5}\right ) y \relax (0)+\left (x -\frac {1}{12} x^{4}-\frac {1}{40} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 49
AsymptoticDSolveValue[y''[x]+(Exp[x]-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {x^5}{40}-\frac {x^4}{12}+x\right )+c_1 \left (-\frac {x^5}{120}-\frac {x^4}{24}-\frac {x^3}{6}+1\right ) \]