67.1.26 problem 2.4 (d)

Internal problem ID [16291]
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 (d)
Date solved : Thursday, October 02, 2025 at 10:45:24 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=6 \\ \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 18

ode=x*D[y[x],x]+2==Sqrt[x]; 
ic={y[1]==6}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 \left (\sqrt {x}-\log (x)+2\right ) \end{align*}

✓ Sympy. Time used: 0.156 (sec). Leaf size: 15

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

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