76.1.20 problem 20

Internal problem ID [17319]
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 : 20
Date solved : Tuesday, January 28, 2025 at 09:59:57 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.103 (sec). Leaf size: 12

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

\[ y = \frac {\ln \left (x^{3}-7\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.359 (sec). Leaf size: 15

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

\[ y(x)\to \frac {1}{3} \log \left (x^3-7\right ) \]