85.19.3 problem 3

Internal problem ID [22560]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 52
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:51:29 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = \frac {{\mathrm e}^{-x^{3}} c_1 -1}{x} \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \frac {-1+c_1 e^{-x^3}}{x} \end{align*}

✓ Sympy. Time used: 0.188 (sec). Leaf size: 12

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

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