68.4.33 problem 33

Internal problem ID [17213]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 33
Date solved : Thursday, October 02, 2025 at 01:54:56 PM
CAS classification : [_separable]

\begin{align*} 4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 28

ode:=4*(x-1)^2*diff(y(x),x)-3*(3+y(x))^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-9 x +9\right ) c_1 -4 x +13}{-3+\left (3 x -3\right ) c_1} \]

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 37

ode=4*(x-1)^2*D[y[x],x]-3*(y[x]+3)^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-4 (1+3 c_1) x+13+12 c_1}{-3+4 c_1 (x-1)}\\ y(x)&\to -3 \end{align*}

✓ Sympy. Time used: 0.179 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*(x - 1)**2*Derivative(y(x), x) - 3*(y(x) + 3)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} x - C_{1} + 4 x - 13}{- 4 C_{1} x + 4 C_{1} + 3} \]