12.3.14 problem 15

Internal problem ID [1591]
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
Date solved : Monday, January 27, 2025 at 05:12:34 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+2 x \left (y+1\right )&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 14

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

\[ y = -1+3 \,{\mathrm e}^{-x^{2}} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 16

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

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