85.15.1 problem 1 (a)

Internal problem ID [22526]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 47
Problem number : 1 (a)
Date solved : Thursday, October 02, 2025 at 08:46:28 PM
CAS classification : [_separable]

\begin{align*} 3 x +4 y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 45

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

\begin{align*} y(x)&\to -\frac {1}{2} \sqrt {-3 x^2+8 c_1}\\ y(x)&\to \frac {1}{2} \sqrt {-3 x^2+8 c_1} \end{align*}

✓ Sympy. Time used: 0.192 (sec). Leaf size: 26

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

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