38.2.24 problem 24

Internal problem ID [8242]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 24
Date solved : Tuesday, September 30, 2025 at 05:19:48 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y-x \right ) y^{\prime }&=y+x \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 49

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

\begin{align*} y &= \frac {c_1 x -\sqrt {2 x^{2} c_1^{2}+1}}{c_1} \\ y &= \frac {c_1 x +\sqrt {2 x^{2} c_1^{2}+1}}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.251 (sec). Leaf size: 86

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

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

✓ Sympy. Time used: 0.698 (sec). Leaf size: 27

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

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