Internal problem ID [44]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x} y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2 \,{\mathrm e}] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 9
dsolve([diff(y(x),x) = exp(x)*y(x),y(0) = 2*exp(1)],y(x), singsol=all)
\[ y \relax (x ) = 2 \,{\mathrm e}^{{\mathrm e}^{x}} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 12
DSolve[{y'[x] == Exp[x]*y[x],y[0]==2*Exp[1]},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 e^{e^x} \\ \end{align*}