30.5.2 problem 2

Internal problem ID [7501]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.6, Substitutions and Transformations. Exercises. page 76
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 04:40:09 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 31

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

\[ y = \frac {c_1 \left (4 x -1\right ) {\mathrm e}^{4 x}-4 x -3}{-1+{\mathrm e}^{4 x} c_1} \]

✓ Mathematica. Time used: 0.104 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to 4 x+\frac {1}{\frac {1}{4}+c_1 e^{4 x}}-1\\ y(x)&\to 4 x-1 \end{align*}

✓ Sympy. Time used: 0.213 (sec). Leaf size: 31

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

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