44.5.10 problem 10

Internal problem ID [7072]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 10
Date solved : Sunday, March 30, 2025 at 11:37:40 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\left (2 y+3\right )^{2}}{\left (4 x +5\right )^{2}} \end{align*}

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

ode:=diff(y(x),x) = (2*y(x)+3)^2/(4*x+5)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-48 x -60\right ) c_1 -8 x -7}{-2+\left (32 x +40\right ) c_1} \]

✓ Mathematica. Time used: 0.285 (sec). Leaf size: 42

ode=D[y[x],x]==( (2*y[x]+3)/(4*x+5))^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {8 (1+6 c_1) x+7+60 c_1}{-2+8 c_1 (4 x+5)} \\ y(x)\to -\frac {3}{2} \\ \end{align*}

✓ Sympy. Time used: 0.361 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (2*y(x) + 3)**2/(4*x + 5)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {- 48 C_{1} x - 60 C_{1} - 8 x - 7}{2 \left (16 C_{1} x + 20 C_{1} - 1\right )} \]