85.2.8 problem 7

Internal problem ID [22435]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. B Exercises at page 14
Problem number : 7
Date solved : Thursday, October 02, 2025 at 08:39:21 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3-x}{y+5} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 43

ode:=diff(y(x),x) = (-x+3)/(y(x)+5); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -5-\sqrt {-x^{2}-2 c_1 +6 x +25} \\ y &= -5+\sqrt {-x^{2}-2 c_1 +6 x +25} \\ \end{align*}

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 51

ode=D[y[x],{x,1}]==(3-x)/(y[x]+5); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -5-\sqrt {-x^2+6 x+25+2 c_1}\\ y(x)&\to -5+\sqrt {-x^2+6 x+25+2 c_1} \end{align*}

✓ Sympy. Time used: 0.248 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(3 - x)/(y(x) + 5) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} - x^{2} + 6 x} - 5, \ y{\left (x \right )} = \sqrt {C_{1} - x^{2} + 6 x} - 5\right ] \]