78.1.1 problem 1.a

Internal problem ID [20927]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 1, First order ODEs. Problems section 1.5
Problem number : 1.a
Date solved : Thursday, October 02, 2025 at 06:49:16 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}}{2 y} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 21

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

\begin{align*} y &= \sqrt {{\mathrm e}^{x}+c_1} \\ y &= -\sqrt {{\mathrm e}^{x}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.471 (sec). Leaf size: 35

ode=D[y[x],x]==Exp[x]/(2*y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.156 (sec). Leaf size: 22

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

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