23.1.499 problem 489

Internal problem ID [5106]
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 : 489
Date solved : Tuesday, September 30, 2025 at 11:37:29 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5+3 x -4 y\right ) y^{\prime }&=2+7 x -3 y \end{align*}

✓ Maple. Time used: 0.185 (sec). Leaf size: 33

ode:=(5+3*x-4*y(x))*diff(y(x),x) = 2+7*x-3*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {4-6859 \left (x -\frac {7}{19}\right )^{2} c_1^{2}}+\left (57 x +95\right ) c_1}{76 c_1} \]

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 71

ode=(5+3*x-4*y[x])*D[y[x],x]==2+7*x-3*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} \left (-i \sqrt {19 x^2-14 x-25-16 c_1}+3 x+5\right )\\ y(x)&\to \frac {1}{4} \left (i \sqrt {19 x^2-14 x-25-16 c_1}+3 x+5\right ) \end{align*}

✓ Sympy. Time used: 1.740 (sec). Leaf size: 51

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-7*x + (3*x - 4*y(x) + 5)*Derivative(y(x), x) + 3*y(x) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {3 x}{4} - \frac {\sqrt {C_{1} - 6859 x^{2} + 5054 x}}{76} + \frac {5}{4}, \ y{\left (x \right )} = \frac {3 x}{4} + \frac {\sqrt {C_{1} - 6859 x^{2} + 5054 x}}{76} + \frac {5}{4}\right ] \]