83.43.8 problem Ex 9 page 11

Internal problem ID [19445]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 9 page 11
Date solved : Monday, March 31, 2025 at 07:14:50 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {6 x -2 y-7}{2 x +3 y-6} \end{align*}

✓ Maple. Time used: 0.127 (sec). Leaf size: 33

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

\[ y = \frac {-\sqrt {3+88 \left (x -\frac {3}{2}\right )^{2} c_1^{2}}+\left (-4 x +12\right ) c_1}{6 c_1} \]

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 67

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

\begin{align*} y(x)\to \frac {1}{3} \left (-\sqrt {22 x^2-66 x+9 (4+c_1)}-2 x+6\right ) \\ y(x)\to \frac {1}{3} \left (\sqrt {22 x^2-66 x+9 (4+c_1)}-2 x+6\right ) \\ \end{align*}

✓ Sympy. Time used: 2.395 (sec). Leaf size: 48

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

\[ \left [ y{\left (x \right )} = - \frac {2 x}{3} - \frac {\sqrt {C_{1} + 88 x^{2} - 264 x}}{6} + 2, \ y{\left (x \right )} = - \frac {2 x}{3} + \frac {\sqrt {C_{1} + 88 x^{2} - 264 x}}{6} + 2\right ] \]