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 : Tuesday, March 04, 2025 at 10:41:00 AM
CAS classification : [_separable]

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

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

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

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

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

ode=D[y[x],x]== 1+x+y[x]+x*y[x]; 
DSolve[ode,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*}

✓ Sympy. Time used: 0.305 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) - x - y(x) + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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