32.2.40 problem 41

Internal problem ID [7757]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 41
Date solved : Tuesday, September 30, 2025 at 05:04:53 PM
CAS classification : [_linear]

\begin{align*} \left (-x^{3}+1\right ) y^{\prime }+x^{2} y&=x^{2} \left (-x^{3}+1\right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=(-x^3+1)*diff(y(x),x)+x^2*y(x) = x^2*(-x^3+1); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}}{2}-\frac {1}{2}+\left (x^{3}-1\right )^{{1}/{3}} c_1 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to \frac {1}{2} \left (x^3+2 c_1 \sqrt [3]{x^3-1}-1\right ) \end{align*}

✓ Sympy. Time used: 0.251 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*(1 - x**3) + x**2*y(x) + (1 - x**3)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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