40.1.4 problem 16

Internal problem ID [6572]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 2. Solutions of differential equations. Supplemetary problems. Page 11
Problem number : 16
Date solved : Sunday, March 30, 2025 at 11:07:43 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 2 x^{3} y^{\prime }&=y \left (y^{2}+3 x^{2}\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 43

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

\begin{align*} y &= \frac {\sqrt {\left (-x +c_1 \right ) x}\, x}{-x +c_1} \\ y &= \frac {\sqrt {\left (-x +c_1 \right ) x}\, x}{-c_1 +x} \\ \end{align*}

✓ Mathematica. Time used: 0.197 (sec). Leaf size: 47

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

\begin{align*} y(x)\to -\frac {x^{3/2}}{\sqrt {-x+c_1}} \\ y(x)\to \frac {x^{3/2}}{\sqrt {-x+c_1}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.679 (sec). Leaf size: 26

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

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