78.1.33 problem 3 (a)

Internal problem ID [18088]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 3 (a)
Date solved : Tuesday, January 28, 2025 at 11:25:57 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 12

dsolve([diff(y(x),x)=x*exp(x),y(1) = 3],y(x), singsol=all)
 

\[ y = \left (x -1\right ) {\mathrm e}^{x}+3 \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 14

DSolve[{D[y[x],x]==x*Exp[x],{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (x-1)+3 \]