75.3.28 problem 29

Internal problem ID [19932]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 29
Date solved : Thursday, October 02, 2025 at 05:02:44 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3 x +2 y-7\right ) y^{\prime }&=2 x -3 y+6 \end{align*}

✓ Maple. Time used: 0.124 (sec). Leaf size: 33

ode:=(3*x+2*y(x)-7)*diff(y(x),x) = 2*x-3*y(x)+6; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\sqrt {4+2197 \left (x -\frac {9}{13}\right )^{2} c_1^{2}}+\left (-39 x +91\right ) c_1}{26 c_1} \]

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 65

ode=(3*x+2*y[x]-7)*D[y[x],x]==(2*x-3*y[x]+6); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \left (-\sqrt {13 x^2-18 x+49+4 c_1}-3 x+7\right )\\ y(x)&\to \frac {1}{2} \left (\sqrt {13 x^2-18 x+49+4 c_1}-3 x+7\right ) \end{align*}

✓ Sympy. Time used: 1.761 (sec). Leaf size: 51

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + (3*x + 2*y(x) - 7)*Derivative(y(x), x) + 3*y(x) - 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {3 x}{2} - \frac {\sqrt {C_{1} + 2197 x^{2} - 3042 x}}{26} + \frac {7}{2}, \ y{\left (x \right )} = - \frac {3 x}{2} + \frac {\sqrt {C_{1} + 2197 x^{2} - 3042 x}}{26} + \frac {7}{2}\right ] \]