67.1.38 problem 2.7 b

Internal problem ID [16303]
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 : 2.7 b
Date solved : Thursday, October 02, 2025 at 10:45:32 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {x}{\sqrt {x^{2}+5}} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=7 \\ \end{align*}

✓ Maple. Time used: 0.031 (sec). Leaf size: 13

ode:=diff(y(x),x) = x/(x^2+5)^(1/2); 
ic:=[y(2) = 7]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sqrt {x^{2}+5}+4 \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 16

ode=D[y[x],x]==x/Sqrt[x^2+5]; 
ic={y[2]==7}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {x^2+5}+4 \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x/sqrt(x**2 + 5) + Derivative(y(x), x),0) 
ics = {y(2): 7} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {x^{2} + 5} + 4 \]