85.6.1 problem 3

Internal problem ID [22451]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. Section 1.3. C Exercises at page 22
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:39:44 PM
CAS classification : [_quadrature]

\begin{align*} \left (y^{\prime }-2 x \right ) \left (y^{\prime }-3 x^{2}\right )&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\begin{align*} y &= x^{2}+c_1 \\ y &= x^{3}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 21

ode=(D[y[x],{x,1}]-2*x)*(D[y[x],{x,1}]-3*x^2)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2+c_1\\ y(x)&\to x^3+c_1 \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 17

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

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