88.6.13 problem 14

Internal problem ID [23995]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 38
Problem number : 14
Date solved : Thursday, October 02, 2025 at 09:50:20 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {4 x -3 y-17}{3 x +y-3} \end{align*}

✓ Maple. Time used: 0.153 (sec). Leaf size: 32

ode:=diff(y(x),x) = (4*x-3*y(x)-17)/(3*x+y(x)-3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -3-\frac {3 \left (x -2\right ) c_1 +\sqrt {13 \left (x -2\right )^{2} c_1^{2}+1}}{c_1} \]

✓ Mathematica. Time used: 0.094 (sec). Leaf size: 53

ode=D[y[x],{x,1}]==( 4*x-3*y[x]-17 )/( 3*x+y[x]-3  ); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {13 x^2-52 x+9+c_1}-3 x+3\\ y(x)&\to \sqrt {13 x^2-52 x+9+c_1}-3 x+3 \end{align*}

✓ Sympy. Time used: 1.183 (sec). Leaf size: 41

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (4*x - 3*y(x) - 17)/(3*x + y(x) - 3),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - 3 x - \sqrt {C_{1} + 13 x^{2} - 52 x} + 3, \ y{\left (x \right )} = - 3 x + \sqrt {C_{1} + 13 x^{2} - 52 x} + 3\right ] \]