89.6.28 problem 28

Internal problem ID [24411]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 28
Date solved : Thursday, October 02, 2025 at 10:25:55 PM
CAS classification : [_linear]

\begin{align*} y&=\left (2 x +1\right ) \left (1-y^{\prime }\right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=y(x) = (2*x+1)*(1-diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 x}{3}+\frac {1}{3}+\frac {c_1}{\sqrt {2 x +1}} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 26

ode=y[x]== (2*x+1)*(1-D[y[x],x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.197 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(1 - Derivative(y(x), x))*(2*x + 1) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} \sqrt {2 x + 1} + 4 x^{2} + 4 x + 1}{3 \left (2 x + 1\right )} \]