23.1.53 problem 47

Internal problem ID [4660]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 47
Date solved : Tuesday, September 30, 2025 at 07:38:27 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Riccati]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

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

\[ y = \frac {c_1 \,x^{2}+x^{3}-1}{c_1 +x} \]

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.168 (sec). Leaf size: 15

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

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