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 : Monday, January 27, 2025 at 01:53:03 PM
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*}

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

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

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

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