67.1.14 problem 2.3 (d)

Internal problem ID [16279]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.3 (d)
Date solved : Thursday, October 02, 2025 at 10:45:18 AM
CAS classification : [_quadrature]

\begin{align*} \sqrt {4+x}\, y^{\prime }&=1 \end{align*}

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

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

\[ y = 2 \sqrt {x +4}+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 17

ode=Sqrt[x+4]*D[y[x],x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 \sqrt {x+4}+c_1 \end{align*}

✓ Sympy. Time used: 0.080 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sqrt(x + 4)*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + 2 \sqrt {x + 4} \]