84.8.10 problem 4.18 (b)

Internal problem ID [22122]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 4. Separable first-order differential equations. Supplementary problems
Problem number : 4.18 (b)
Date solved : Thursday, October 02, 2025 at 08:25:34 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

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

\begin{align*} y &= \sqrt {x \,{\mathrm e}^{x}-{\mathrm e}^{x}+c_1} \\ y &= -\sqrt {\left (x -1\right ) {\mathrm e}^{x}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 1.735 (sec). Leaf size: 43

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

\begin{align*} y(x)&\to -\sqrt {e^x (x-1)+2 c_1}\\ y(x)&\to \sqrt {e^x (x-1)+2 c_1} \end{align*}

✓ Sympy. Time used: 0.188 (sec). Leaf size: 32

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

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