73.7.17 problem 17

Internal problem ID [15096]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 17
Date solved : Thursday, March 13, 2025 at 05:37:47 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {1}{x y-3 x} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 35

ode:=diff(y(x),x) = 1/(x*y(x)-3*x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 3-\sqrt {9+2 \ln \left (x \right )+2 c_{1}} \\ y &= 3+\sqrt {9+2 \ln \left (x \right )+2 c_{1}} \\ \end{align*}

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 43

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

\begin{align*} y(x)\to 3-\sqrt {2 \log (x)+9+2 c_1} \\ y(x)\to 3+\sqrt {2 \log (x)+9+2 c_1} \\ \end{align*}

✓ Sympy. Time used: 0.387 (sec). Leaf size: 27

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

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