Internal problem ID [571]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-3+6 x -y+2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 15
dsolve(diff(y(x),x) = 3-6*x+y(x)-2*x*y(x),y(x), singsol=all)
\[ y \relax (x ) = -3+{\mathrm e}^{-x \left (x -1\right )} c_{1} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 24
DSolve[y'[x] == 3-6*x+y[x]-2*x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -3+c_1 e^{x-x^2} \\ y(x)\to -3 \\ \end{align*}