67.1.33 problem 2.6 (a)

Internal problem ID [16298]
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 : 2.6 (a)
Date solved : Thursday, October 02, 2025 at 10:45:29 AM
CAS classification : [_quadrature]

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

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

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

\[ y = \left (2 x +6\right ) \sqrt {x +3}+c_1 \]

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

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

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

✓ Sympy. Time used: 0.076 (sec). Leaf size: 12

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

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