40.4.5 problem 19 (f)

Internal problem ID [6645]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (f)
Date solved : Monday, January 27, 2025 at 02:16:40 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \frac {{\mathrm e}^{-x}}{-x +c_1} \]

✓ Solution by Mathematica

Time used: 0.209 (sec). Leaf size: 25

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

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