76.1.7 problem 7

Internal problem ID [17306]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 09:59:16 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 31

dsolve(y(x)*diff(y(x),x)=(x+x*y(x)^2)*exp(x^2),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: 4.140 (sec). Leaf size: 61

DSolve[y[x]*D[y[x],x]==(x+x*y[x]^2)*Exp[x^2],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*}