2.2.14 problem 18

Internal problem ID [674]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 18
Date solved : Tuesday, September 30, 2025 at 04:05:25 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.061 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 29

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

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

✓ Sympy. Time used: 0.250 (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 = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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