23.1.251 problem 245

Internal problem ID [4858]
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 : 245
Date solved : Tuesday, September 30, 2025 at 08:45:21 AM
CAS classification : [_linear]

\begin{align*} \left (1-2 x \right ) y^{\prime }&=16+32 x -6 y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=(1-2*x)*diff(y(x),x) = 16+32*x-6*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {4}{3}+8 x +\left (-1+2 x \right )^{3} c_1 \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 22

ode=(1-2*x)*D[y[x],x]==2(8+16*x-3*y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 8 x+c_1 (2 x-1)^3+\frac {4}{3} \end{align*}

✓ Sympy. Time used: 0.288 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-32*x + (1 - 2*x)*Derivative(y(x), x) + 6*y(x) - 16,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 8 C_{1} x^{3} - 12 C_{1} x^{2} + 6 C_{1} x - C_{1} + 8 x + \frac {4}{3} \]