85.33.61 problem 61

Internal problem ID [22684]
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 : 61
Date solved : Thursday, October 02, 2025 at 09:06:26 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\left (3+y\right )^{2}}{4 x^{2}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(y(x),x) = 1/4*(3+y(x))^2/x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3+\left (-3 c_1 -4\right ) x}{c_1 x -1} \]

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 31

ode=D[y[x],{x,1}]==((y[x]+3)/(2*x))^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3-4 (1+3 c_1) x}{-1+4 c_1 x}\\ y(x)&\to -3 \end{align*}

✓ Sympy. Time used: 0.128 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (y(x) + 3)**2/(4*x**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {- 12 C_{1} x - 4 x + 3}{4 C_{1} x - 1} \]