28.1.115 problem 138

Internal problem ID [4421]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 138
Date solved : Sunday, March 30, 2025 at 03:21:15 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

\begin{align*} 2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 38

ode:=2*x^3*y(x)*diff(y(x),x)+3*x^2*y(x)^2+7 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.207 (sec). Leaf size: 42

ode=2*x^3*y[x]*D[y[x],x]+3*x^2*y[x]^2+7==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-7 x+c_1}}{x^{3/2}} \\ y(x)\to \frac {\sqrt {-7 x+c_1}}{x^{3/2}} \\ \end{align*}

✓ Sympy. Time used: 0.493 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**3*y(x)*Derivative(y(x), x) + 3*x**2*y(x)**2 + 7,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {\frac {\frac {C_{1}}{x} - 7}{x^{2}}}, \ y{\left (x \right )} = \sqrt {\frac {\frac {C_{1}}{x} - 7}{x^{2}}}\right ] \]