Internal problem ID [42]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-y-y x=x +1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x) = 1+x+y(x)+x*y(x),y(x), singsol=all)
\[ y \left (x \right ) = -1+{\mathrm e}^{\frac {x \left (2+x \right )}{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 25
DSolve[y'[x] == 1+x+y[x]+x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+c_1 e^{\frac {1}{2} x (x+2)} y(x)\to -1 \end{align*}