Internal problem ID [5339]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page
238
Problem number: 1(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime } {\mathrm e}^{x}-{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 14
dsolve(diff(y(x),x$2)+exp(x)*diff(y(x),x)=exp(x),y(x), singsol=all)
\[ y \relax (x ) = -c_{1} \expIntegral \left (1, {\mathrm e}^{x}\right )+x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 18
DSolve[y''[x]+Exp[x]*y'[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \text {ExpIntegralEi}\left (-e^x\right )+x+c_2 \\ \end{align*}