85.14.5 problem 4

Internal problem ID [22521]
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. C Exercises at page 41
Problem number : 4
Date solved : Thursday, October 02, 2025 at 08:45:29 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 2+3 x y^{2}-4 x^{2} y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 47

ode:=2+3*x*y(x)^2-4*x^2*y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\sqrt {5}\, \sqrt {5 x^{{7}/{2}} c_1 -2 x}}{5 x} \\ y &= \frac {\sqrt {5}\, \sqrt {5 x^{{7}/{2}} c_1 -2 x}}{5 x} \\ \end{align*}

✓ Mathematica. Time used: 3.603 (sec). Leaf size: 51

ode=(2+3*x*y[x]^2)-(4*x^2*y[x])*D[y[x],x]==  0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {-\frac {2}{5 x}+c_1 x^{3/2}}\\ y(x)&\to \sqrt {-\frac {2}{5 x}+c_1 x^{3/2}} \end{align*}

✓ Sympy. Time used: 0.356 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**2*y(x)*Derivative(y(x), x) + 3*x*y(x)**2 + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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