7.5.32 problem 32

Internal problem ID [136]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 32
Date solved : Tuesday, March 04, 2025 at 10:52:08 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 51

ode:=4*x-y(x)+(6*y(x)-x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {c_1 x -\sqrt {-23 c_1^{2} x^{2}+12}}{6 c_1} \\ y &= \frac {c_1 x +\sqrt {-23 c_1^{2} x^{2}+12}}{6 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.486 (sec). Leaf size: 106

ode=(4*x-y[x])+(6*y[x]-x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{6} \left (x-\sqrt {-23 x^2+12 e^{c_1}}\right ) \\ y(x)\to \frac {1}{6} \left (x+\sqrt {-23 x^2+12 e^{c_1}}\right ) \\ y(x)\to \frac {1}{6} \left (x-\sqrt {23} \sqrt {-x^2}\right ) \\ y(x)\to \frac {1}{6} \left (\sqrt {23} \sqrt {-x^2}+x\right ) \\ \end{align*}

✓ Sympy. Time used: 1.317 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x + (-x + 6*y(x))*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {x}{6} - \frac {\sqrt {C_{1} - 23 x^{2}}}{6}, \ y{\left (x \right )} = \frac {x}{6} + \frac {\sqrt {C_{1} - 23 x^{2}}}{6}\right ] \]