Internal problem ID [66]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y+y^{\prime }-{\mathrm e}^{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 15
dsolve([y(x)+diff(y(x),x) = exp(x),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 7
DSolve[{y[x]+y'[x] == Exp[x],y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cosh (x) \\ \end{align*}