36.1.24 problem 24

Internal problem ID [6279]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 24
Date solved : Sunday, March 30, 2025 at 10:48:34 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=8 x^{3} {\mathrm e}^{-2 y} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Maple. Time used: 0.103 (sec). Leaf size: 14

ode:=diff(y(x),x) = 8*x^3*exp(-2*y(x)); 
ic:=y(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {\ln \left (4 x^{4}-3\right )}{2} \]

✓ Mathematica. Time used: 0.372 (sec). Leaf size: 17

ode=D[y[x],x]==8*x^3*Exp[-2*y[x]]; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} \log \left (4 x^4-3\right ) \]

✓ Sympy. Time used: 0.368 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**3*exp(-2*y(x)) + Derivative(y(x), x),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\log {\left (4 x^{4} - 3 \right )}}{2} \]