88.12.6 problem 8

Internal problem ID [24062]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:56:38 PM
CAS classification : [_separable]

\begin{align*} x^{2} y^{5}+{\mathrm e}^{x^{3}} y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.073 (sec). Leaf size: 21

ode:=x^2*y(x)^5+exp(x^3)*diff(y(x),x) = 0; 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2 \sqrt {3}}{\left (201-192 \,{\mathrm e}^{-x^{3}}\right )^{{1}/{4}}} \]

✓ Mathematica. Time used: 3.813 (sec). Leaf size: 34

ode=(x^2*y[x]^5)+Exp[x^3]*D[y[x],{x,1}]==0; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 \sqrt [4]{-3} e^{\frac {x^3}{4}}}{\sqrt [4]{64-67 e^{x^3}}} \end{align*}

✓ Sympy. Time used: 2.264 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*y(x)**5 + exp(x**3)*Derivative(y(x), x),0) 
ics = {y(0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt [4]{3} \sqrt [4]{- \frac {e^{x^{3}}}{4 - \frac {67 e^{x^{3}}}{16}}} \]