30.6.30 problem 31

Internal problem ID [7565]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 31
Date solved : Tuesday, September 30, 2025 at 04:53:07 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 12

ode:=x^3-y(x)+x*diff(y(x),x) = 0; 
ic:=[y(1) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {\left (x^{2}-7\right ) x}{2} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 15

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

\begin{align*} y(x)&\to -\frac {1}{2} x \left (x^2-7\right ) \end{align*}

✓ Sympy. Time used: 0.149 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = x \left (\frac {7}{2} - \frac {x^{2}}{2}\right ) \]