76.5.25 problem 26

Internal problem ID [17445]
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 2.7 (Substitution Methods). Problems at page 108
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 10:37:53 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

\begin{align*} y^{\prime }-4 \,{\mathrm e}^{x} y^{2}&=y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(diff(y(x),x)-4*exp(x)*y(x)^2=y(x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x}}{-2 \,{\mathrm e}^{2 x}+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.219 (sec). Leaf size: 29

DSolve[D[y[x],x]-4*Exp[x]*y[x]^2==y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {e^x}{2 e^{2 x}-c_1} \\ y(x)\to 0 \\ \end{align*}