71.8.10 problem 5 (c)

Internal problem ID [14444]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 5 (c)
Date solved : Tuesday, January 28, 2025 at 06:31:19 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 11

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

\[ y = -\frac {1}{x -3} \]

✓ Solution by Mathematica

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

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

\[ y(x)\to \frac {1}{3-x} \]