44.4.24 problem 8 (b)

Internal problem ID [7037]
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 (b)
Date solved : Wednesday, March 05, 2025 at 04:03:30 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (-2\right )&=-1 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 13

ode:=diff(y(x),x) = 1/y(x); 
ic:=y(-2) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\sqrt {2 x +5} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 16

ode=D[y[x],x]==1/y[x]; 
ic={y[-2]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\sqrt {2 x+5} \]

✓ Sympy. Time used: 0.294 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/y(x),0) 
ics = {y(-2): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \sqrt {2 x + 5} \]