85.33.32 problem 32

Internal problem ID [22655]
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. A Exercises at page 65
Problem number : 32
Date solved : Thursday, October 02, 2025 at 09:02:57 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = \left (x +c_1 \right ) x^{2} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to x^2 (x+c_1) \end{align*}

✓ Sympy. Time used: 0.138 (sec). Leaf size: 8

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

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