87.3.12 problem 12

Internal problem ID [23261]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 26
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:27:20 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

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

\begin{align*} y &= 0 \\ y &= c_1 \,{\mathrm e}^{\frac {\left (x^{2}+1\right )^{2}}{4}} \\ \end{align*}

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to 0\\ y(x)&\to c_1 e^{\frac {1}{4} x^2 \left (x^2+2\right )}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.345 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x^{2} \left (x^{2} + 2\right )}{4}} \]