35.2.8 problem 8

Internal problem ID [6100]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 2. Separable equations. page 398
Problem number : 8
Date solved : Monday, January 27, 2025 at 01:36:08 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+2 x y^{2}&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 11

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

\[ y = \frac {1}{x^{2}-3} \]

✓ Solution by Mathematica

Time used: 0.150 (sec). Leaf size: 12

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

\[ y(x)\to \frac {1}{x^2-3} \]