15.8.25 problem 26

Internal problem ID [3028]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 26
Date solved : Sunday, March 30, 2025 at 01:11:12 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 31

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

\begin{align*} y &= \sqrt {-12 \ln \left (x \right )+c_1 +6 x} \\ y &= -\sqrt {-12 \ln \left (x \right )+c_1 +6 x} \\ \end{align*}

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 50

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

\begin{align*} y(x)\to -\sqrt {2} \sqrt {3 x-6 \log (x)+c_1} \\ y(x)\to \sqrt {2} \sqrt {3 x-6 \log (x)+c_1} \\ \end{align*}

✓ Sympy. Time used: 0.363 (sec). Leaf size: 32

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

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} + 6 x - 12 \log {\left (x \right )}}, \ y{\left (x \right )} = \sqrt {C_{1} + 6 x - 12 \log {\left (x \right )}}\right ] \]