28.1.5 problem 5

Internal problem ID [4311]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 5
Date solved : Monday, January 27, 2025 at 09:01:23 AM
CAS classification : [_separable]

\begin{align*} x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 33

dsolve(x*y(x)^3+exp(x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {c_{1} -{\mathrm e}^{-x^{2}}}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {c_{1} -{\mathrm e}^{-x^{2}}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 7.351 (sec). Leaf size: 70

DSolve[x*y[x]^3+Exp[x^2]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {i e^{\frac {x^2}{2}}}{\sqrt {1+2 c_1 e^{x^2}}} \\ y(x)\to \frac {i e^{\frac {x^2}{2}}}{\sqrt {1+2 c_1 e^{x^2}}} \\ y(x)\to 0 \\ \end{align*}