38.4.23 problem 8 (a)

Internal problem ID [8322]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 8 (a)
Date solved : Tuesday, September 30, 2025 at 05:26:29 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.050 (sec). Leaf size: 11

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

\[ y = \sqrt {2 x +1} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Sympy. Time used: 0.164 (sec). Leaf size: 10

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

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