67.1.13 problem 2.3 (c)

Internal problem ID [16278]
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 (c)
Date solved : Thursday, October 02, 2025 at 10:45:17 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.153 (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 = {} 
dsolve(ode,func=y(x),ics=ics)
 

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