12.6.23 problem 23

Internal problem ID [1702]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 23
Date solved : Saturday, March 29, 2025 at 11:35:00 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 7 x +4 y+\left (4 x +3 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 53

ode:=7*x+4*y(x)+(4*x+3*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-4 c_1 x -\sqrt {-5 x^{2} c_1^{2}+3}}{3 c_1} \\ y &= \frac {-4 c_1 x +\sqrt {-5 x^{2} c_1^{2}+3}}{3 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.438 (sec). Leaf size: 118

ode=(7*x+4*y[x])+(4*x+3*y[x])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{3} \left (-4 x-\sqrt {-5 x^2+3 e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{3} \left (-4 x+\sqrt {-5 x^2+3 e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{3} \left (-\sqrt {5} \sqrt {-x^2}-4 x\right ) \\ y(x)\to \frac {1}{3} \left (\sqrt {5} \sqrt {-x^2}-4 x\right ) \\ \end{align*}

✓ Sympy. Time used: 1.334 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(7*x + (4*x + 3*y(x))*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {x \left (\sqrt {\frac {C_{1}}{x^{2}} - 5} - 4\right )}{3}, \ y{\left (x \right )} = \frac {x \left (- \sqrt {\frac {C_{1}}{x^{2}} - 5} - 4\right )}{3}\right ] \]