87.6.15 problem 18

Internal problem ID [23332]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 53
Problem number : 18
Date solved : Thursday, October 02, 2025 at 09:37:46 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {3 x -2 y+7}{2 x +3 y+9} \end{align*}

✓ Maple. Time used: 0.103 (sec). Leaf size: 33

ode:=diff(y(x),x) = (3*x-2*y(x)+7)/(2*x+3*y(x)+9); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {13 \left (x +3\right )^{2} c_1^{2}+3}+\left (-2 x -9\right ) c_1}{3 c_1} \]

✓ Mathematica. Time used: 0.084 (sec). Leaf size: 67

ode=D[y[x],x]==(3*x-2*y[x]+7)/(2*x+3*y[x]+9); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} \left (-\sqrt {13 x^2+78 x+9 (9+c_1)}-2 x-9\right )\\ y(x)&\to \frac {1}{3} \left (\sqrt {13 x^2+78 x+9 (9+c_1)}-2 x-9\right ) \end{align*}

✓ Sympy. Time used: 1.432 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (3*x - 2*y(x) + 7)/(2*x + 3*y(x) + 9),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {2 x}{3} - \frac {\sqrt {C_{1} + 13 x^{2} + 78 x}}{3} - 3, \ y{\left (x \right )} = - \frac {2 x}{3} + \frac {\sqrt {C_{1} + 13 x^{2} + 78 x}}{3} - 3\right ] \]