32.5.4 problem Exercise 11.4, page 97

Internal problem ID [5842]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.4, page 97
Date solved : Monday, January 27, 2025 at 01:20:23 PM
CAS classification : [_linear]

\begin{align*} x^{\prime }+2 y x&={\mathrm e}^{-y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

dsolve(diff(x(y),y)+2*y*x(y)=exp(-y^2),x(y), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 17

DSolve[D[x[y],y]+2*y*x[y]==Exp[-y^2],x[y],y,IncludeSingularSolutions -> True]
 

\[ x(y)\to e^{-y^2} (y+c_1) \]