84.7.5 problem 4.5

Internal problem ID [22111]
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. Solved problems. Page 14
Problem number : 4.5
Date solved : Thursday, October 02, 2025 at 08:25:13 PM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{x}-y y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 12

ode:=exp(x)-y(x)*diff(y(x),x) = 0; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sqrt {2 \,{\mathrm e}^{x}-1} \]

✓ Mathematica. Time used: 0.48 (sec). Leaf size: 16

ode=Exp[x]-y[x]*D[y[x],x]==0; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.250 (sec). Leaf size: 12

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

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