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 : Tuesday, March 04, 2025 at 06:20:04 PM
CAS classification : [_separable]

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

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

ode:=x*y(x)^3+exp(x^2)*diff(y(x),x) = 0; 
dsolve(ode,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*}

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

ode=x*y[x]^3+Exp[x^2]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.842 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)**3 + exp(x**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {- \frac {e^{x^{2}}}{C_{1} e^{x^{2}} + 1}}, \ y{\left (x \right )} = \sqrt {- \frac {e^{x^{2}}}{C_{1} e^{x^{2}} + 1}}\right ] \]