Internal problem ID [3150]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{3} x +y^{\prime } {\mathrm e}^{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (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 {-{\mathrm e}^{-x^{2}}+c_{1}}} y \left (x \right ) = -\frac {1}{\sqrt {-{\mathrm e}^{-x^{2}}+c_{1}}} \end{align*}
✓ Solution by Mathematica
Time used: 7.124 (sec). Leaf size: 70
DSolve[x*y[x]^3+Exp[x^2]*y'[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*}