73.1.24 problem 2.4 (b)

Internal problem ID [14931]
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 : 2.4 (b)
Date solved : Monday, March 31, 2025 at 01:04:17 PM
CAS classification : [_quadrature]

\begin{align*} \left (x +6\right )^{{1}/{3}} y^{\prime }&=1 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=10 \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 13

ode:=(x+6)^(1/3)*diff(y(x),x) = 1; 
ic:=y(2) = 10; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {3 \left (x +6\right )^{{2}/{3}}}{2}+4 \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 18

ode=(x+6)^(1/3)*D[y[x],x]==1; 
ic={y[2]==10}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {3}{2} (x+6)^{2/3}+4 \]

✓ Sympy. Time used: 0.148 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 6)**(1/3)*Derivative(y(x), x) - 1,0) 
ics = {y(2): 10} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 \left (x + 6\right )^{\frac {2}{3}}}{2} + 4 \]