Internal problem ID [5302]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Bernoulli]
\[ \boxed {y+y^{\prime }-{\mathrm e}^{x} y^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve(diff(y(x),x)+y(x)=y(x)^2*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-x}}{-x +c_{1}} \]
✓ Solution by Mathematica
Time used: 0.204 (sec). Leaf size: 25
DSolve[y'[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*}