84.14.6 problem 7.14

Internal problem ID [22163]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 7. Integrating factors. Supplementary problems
Problem number : 7.14
Date solved : Thursday, October 02, 2025 at 08:33:06 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 26

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

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

✓ Sympy. Time used: 0.258 (sec). Leaf size: 12

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

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