Internal problem ID [4801]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.1.2 page
230
Problem number: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime } {\mathrm e}^{x}-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: 49
Order:=6; dsolve(diff(y(x),x$2)+exp(x)*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{2} x^{2}-\frac {1}{6} x^{3}-\frac {1}{120} x^{5}\right ) y \relax (0)+\left (x -\frac {1}{2} x^{2}+\frac {1}{6} x^{3}-\frac {1}{24} x^{4}+\frac {1}{120} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 63
AsymptoticDSolveValue[y''[x]+Exp[x]*y'[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^5}{120}-\frac {x^3}{6}+\frac {x^2}{2}+1\right )+c_2 \left (\frac {x^5}{120}-\frac {x^4}{24}+\frac {x^3}{6}-\frac {x^2}{2}+x\right ) \]