76.5.1 problem 1

Internal problem ID [17350]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 1
Date solved : Monday, March 31, 2025 at 03:55:45 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

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

\begin{align*} y &= \sqrt {x^{2}+c_1 +2 x} \\ y &= -\sqrt {x^{2}+c_1 +2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 41

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

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

✓ Sympy. Time used: 0.335 (sec). Leaf size: 29

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

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