89.10.25 problem 25

Internal problem ID [24518]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 77
Problem number : 25
Date solved : Thursday, October 02, 2025 at 10:44:53 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x -3 y+1-\left (3 x +2 y-4\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.098 (sec). Leaf size: 33

ode:=2*x-3*y(x)+1-(3*x+2*y(x)-4)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {4+2197 \left (x -\frac {10}{13}\right )^{2} c_1^{2}}+\left (-39 x +52\right ) c_1}{26 c_1} \]

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 67

ode=(2*x-3*y[x]+1 )-( 3*x+2*y[x]-4 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \left (-\sqrt {13 x^2-20 x+4 (4+c_1)}-3 x+4\right )\\ y(x)&\to \frac {1}{2} \left (\sqrt {13 x^2-20 x+4 (4+c_1)}-3 x+4\right ) \end{align*}

✓ Sympy. Time used: 1.624 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x - (3*x + 2*y(x) - 4)*Derivative(y(x), x) - 3*y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {3 x}{2} - \frac {\sqrt {C_{1} + 2197 x^{2} - 3380 x}}{26} + 2, \ y{\left (x \right )} = - \frac {3 x}{2} + \frac {\sqrt {C_{1} + 2197 x^{2} - 3380 x}}{26} + 2\right ] \]