23.1.58 problem 52

Internal problem ID [4665]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 52
Date solved : Tuesday, September 30, 2025 at 07:50:28 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 32

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

\[ y = \frac {c_1 \left (2 x +5\right ) {\mathrm e}^{4 x}-2 x -7}{8 \,{\mathrm e}^{4 x} c_1 -8} \]

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 41

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

\begin{align*} y(x)&\to \frac {1}{16} \left (4 x+\frac {1}{\frac {1}{4}+c_1 e^{4 x}}+10\right )\\ y(x)&\to \frac {1}{8} (2 x+5) \end{align*}

✓ Sympy. Time used: 0.222 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = \frac {2 C_{1} x + 7 C_{1} - 2 x e^{4 x} - 5 e^{4 x}}{8 \left (C_{1} - e^{4 x}\right )} \]