22.1.17 problem 17

Internal problem ID [4323]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 07:18:16 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y+2&=\left (2 x +y-4\right ) y^{\prime } \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 49

ode:=y(x)+2 = (2*x+y(x)-4)*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1-4 c_1 +\sqrt {1+4 \left (x -3\right ) c_1}}{2 c_1} \\ y &= \frac {1-4 c_1 -\sqrt {1+4 \left (x -3\right ) c_1}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.146 (sec). Leaf size: 82

ode=y[x]+2==(2*x+y[x]-4)*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\sqrt {1+4 c_1 (x-3)}-1+4 c_1}{2 c_1}\\ y(x)&\to \frac {\sqrt {1+4 c_1 (x-3)}+1-4 c_1}{2 c_1}\\ y(x)&\to -2\\ y(x)&\to \text {Indeterminate}\\ y(x)&\to 1-x \end{align*}

✓ Sympy. Time used: 1.291 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-2*x - y(x) + 4)*Derivative(y(x), x) + y(x) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {C_{1}}{2} - \frac {\sqrt {C_{1} \left (C_{1} + 4 x - 12\right )}}{2} - 2, \ y{\left (x \right )} = \frac {C_{1}}{2} + \frac {\sqrt {C_{1} \left (C_{1} + 4 x - 12\right )}}{2} - 2\right ] \]