Internal problem ID [4427]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-8 x^{3} {\mathrm e}^{-2 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 14
dsolve([diff(y(x),x)=8*x^3*exp(-2*y(x)),y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (4 x^{4}-3\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.517 (sec). Leaf size: 17
DSolve[{y'[x]==8*x^3*Exp[-2*y[x]],{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \log \left (4 x^4-3\right ) \\ \end{align*}