36.1.15 problem 15

Internal problem ID [6270]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 15
Date solved : Monday, January 27, 2025 at 01:52:32 PM
CAS classification : [_separable]

\begin{align*} x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 35

dsolve((x+x*y(x)^2)+exp(x^2)*y(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {{\mathrm e}^{{\mathrm e}^{-x^{2}}} c_{1} -1} \\ y &= -\sqrt {{\mathrm e}^{{\mathrm e}^{-x^{2}}} c_{1} -1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 4.215 (sec). Leaf size: 65

DSolve[(x+x*y[x]^2)+Exp[x^2]*y[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-1+e^{e^{-x^2}+2 c_1}} \\ y(x)\to \sqrt {-1+e^{e^{-x^2}+2 c_1}} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}