7.4.20 problem 20

Internal problem ID [92]
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 1.5 (linear equations). Problems at page 54
Problem number : 20
Date solved : Tuesday, March 04, 2025 at 10:42:55 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 13

ode:=diff(y(x),x) = 1+x+y(x)+x*y(x); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 17

ode=D[y[x],x]==1+x+y[x]+x*y[x]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{\frac {1}{2} x (x+2)}-1 \]

✓ Sympy. Time used: 0.284 (sec). Leaf size: 12

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

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