8.3.18 problem 19

Internal problem ID [694]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 19
Date solved : Monday, January 27, 2025 at 02:58:13 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{x} y \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \,{\mathrm e} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 9

dsolve([diff(y(x),x) = exp(x)*y(x),y(0) = 2*exp(1)],y(x), singsol=all)
 

\[ y = 2 \,{\mathrm e}^{{\mathrm e}^{x}} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 12

DSolve[{D[y[x],x] == Exp[x]*y[x],y[0]==2*Exp[1]},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 e^{e^x} \]