Internal problem ID [941]
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: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+2 x \left (1+y\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 14
dsolve([diff(y(x),x)+2*x*(y(x)+1)=0,y(0) = 2],y(x), singsol=all)
\[ y \relax (x ) = -1+3 \,{\mathrm e}^{-x^{2}} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 16
DSolve[{y'[x]+2*x*(y[x]+1)==0,y[0]==2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 e^{-x^2}-1 \\ \end{align*}