85.12.3 problem 3

Internal problem ID [22497]
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 40
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:42:51 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = c_1 \,x^{3}-x \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 15

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

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

✓ Sympy. Time used: 0.137 (sec). Leaf size: 10

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

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