44.2.31 problem 31 (a)

Internal problem ID [6963]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 31 (a)
Date solved : Monday, January 27, 2025 at 02:38:52 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 11

dsolve([diff(y(x),x)=y(x)^2,y(0) = 1],y(x), singsol=all)
 

\[ y = -\frac {1}{x -1} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 12

DSolve[{D[y[x],x]==y[x]^2,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{1-x} \]