12.3.11 problem 12

Internal problem ID [1588]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number : 12
Date solved : Monday, January 27, 2025 at 05:09:35 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 19

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

\[ y = \frac {1}{-1+2 \,{\mathrm e}^{\frac {\left (x -2\right ) \left (x +2\right )}{2}}} \]

✓ Solution by Mathematica

Time used: 0.217 (sec). Leaf size: 27

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

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