32.2.2 problem 2

Internal problem ID [7719]
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 : 2
Date solved : Tuesday, September 30, 2025 at 05:02:02 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 15

ode:=(x^3+1)*diff(y(x),x) = x^2*y(x); 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to 2^{2/3} \sqrt [3]{x^3+1} \end{align*}

✓ Sympy. Time used: 0.145 (sec). Leaf size: 15

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

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