76.1.8 problem 8

Internal problem ID [17307]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 09:59:19 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

dsolve(diff(y(x),x)=(x^2+exp(-x))/(y(x)^2-exp(y(x))),y(x), singsol=all)
 

\[ \frac {x^{3}}{3}-{\mathrm e}^{-x}-\frac {y^{3}}{3}+{\mathrm e}^{y}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.616 (sec). Leaf size: 35

DSolve[D[y[x],x]==(x^2+Exp[-x])/(y[x]^2-Exp[y[x]]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [e^{\text {$\#$1}}-\frac {\text {$\#$1}^3}{3}\&\right ]\left [-\frac {x^3}{3}+e^{-x}+c_1\right ] \]