7.3.17 problem 17

Internal problem ID [57]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 17
Date solved : Friday, February 07, 2025 at 07:47:17 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=1+x +y+x y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(diff(y(x),x)= 1+x+y(x)+x*y(x),y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{\frac {x \left (x +2\right )}{2}}-1 \]

✓ Solution by Mathematica

Time used: 0.156 (sec). Leaf size: 25

DSolve[D[y[x],x]== 1+x+y[x]+x*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -1+c_1 e^{\frac {1}{2} x (x+2)} \\ y(x)\to -1 \\ \end{align*}