76.5.28 problem 29

Internal problem ID [17377]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 29
Date solved : Monday, March 31, 2025 at 04:10:28 PM
CAS classification : [_separable]

\begin{align*} \frac {\sqrt {x}\, y^{\prime }}{y}&=1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = c_1 \,{\mathrm e}^{2 \sqrt {x}} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 17

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

\[ y(x)\to c_1 e^{2 \sqrt {x}} \]

✓ Sympy. Time used: 0.211 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} e^{2 \sqrt {x}} \]