6.3.14 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 : Tuesday, September 30, 2025 at 04:38:48 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*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 14

ode:=diff(y(x),x)+2*x*(y(x)+1) = 0; 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to 3 e^{-x^2}-1 \end{align*}

✓ Sympy. Time used: 0.170 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*(y(x) + 1) + Derivative(y(x), x),0) 
ics = {y(0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = -1 + 3 e^{- x^{2}} \]