2.4.20 problem 20

Internal problem ID [723]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 04:07:08 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: 0.024 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.019 (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]
 

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

✓ Sympy. Time used: 0.170 (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)
 

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