Internal problem ID [15050]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 157.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+2 y x -2 y^{2} x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)+2*x*y(x)=2*x*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{1+{\mathrm e}^{x^{2}} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.204 (sec). Leaf size: 27
DSolve[y'[x]+2*x*y[x]==2*x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{1+e^{x^2+c_1}} \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}