85.26.2 problem 2

Internal problem ID [22590]
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. C Exercises at page 57
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:53:46 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

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

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

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

\begin{align*} y(x)&\to \frac {x^2 (x+c_1)}{x^2+1} \end{align*}

✓ Sympy. Time used: 0.159 (sec). Leaf size: 14

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

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