85.1.6 problem 1 (h)

Internal problem ID [22411]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 1 (h)
Date solved : Thursday, October 02, 2025 at 08:38:36 PM
CAS classification : [_linear]

\begin{align*} 2 x +y+\left (x -3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=2*x+y(x)+(x-3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-x^{2}+c_1}{x -3} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 19

ode=(2*x+y[x])+(x-3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^2+c_1}{3-x} \end{align*}

✓ Sympy. Time used: 0.117 (sec). Leaf size: 10

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

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