Internal problem ID [938]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+x \left (y^{2}+y\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 19
dsolve([diff(y(x),x)+x*(y(x)^2+y(x))=0,y(2) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{-1+2 \,{\mathrm e}^{\frac {\left (-2+x \right ) \left (2+x \right )}{2}}} \]
✓ Solution by Mathematica
Time used: 0.247 (sec). Leaf size: 22
DSolve[{y'[x]+x*(y[x]^2+y[x])==0,y[2]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2 e^{\frac {x^2}{2}-2}-1} \\ \end{align*}