Internal problem ID [975]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: Example 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-y-x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 17
dsolve(diff(y(x),x)-y(x)=x*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{1+{\mathrm e}^{-x} c_{1}-x} \]
✓ Solution by Mathematica
Time used: 0.121 (sec). Leaf size: 25
DSolve[y'[x]-y[x]==x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-x+c_1 e^{-x}+1} \\ y(x)\to 0 \\ \end{align*}