64.6.11 problem 11

Internal problem ID [13282]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 11
Date solved : Wednesday, March 05, 2025 at 09:33:23 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 x -7 y}{3 y-8 x} \end{align*}

✓ Maple. Time used: 0.111 (sec). Leaf size: 47

ode:=diff(y(x),x) = (2*x-7*y(x))/(3*y(x)-8*x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-12 c_{1} x -\sqrt {-60 c_{1} x +1}+1}{18 c_{1}} \\ y &= \frac {-12 c_{1} x +1+\sqrt {-60 c_{1} x +1}}{18 c_{1}} \\ \end{align*}

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 44

ode=D[y[x],x]==(2*x-7*y[x])/(3*y[x]-8*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {3 K[1]-8}{(K[1]-1) (3 K[1]+2)}dK[1]=-\log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 2.131 (sec). Leaf size: 53

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (2*x - 7*y(x))/(-8*x + 3*y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {2 C_{1}}{9} - \frac {2 x}{3} - \frac {2 \sqrt {C_{1} \left (C_{1} + 15 x\right )}}{9}, \ y{\left (x \right )} = - \frac {2 C_{1}}{9} - \frac {2 x}{3} + \frac {2 \sqrt {C_{1} \left (C_{1} + 15 x\right )}}{9}\right ] \]