7.3.29 problem 29

Internal problem ID [69]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 29
Date solved : Friday, February 07, 2025 at 07:47:44 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (a \right )&=b \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 17

dsolve([diff(y(x),x)= y(x)^2,y(a) = b],y(x), singsol=all)
 

\[ y = \frac {b}{1+\left (a -x \right ) b} \]

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 18

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

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