Internal problem ID [73]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-1-x -y-y x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 13
dsolve([diff(y(x),x) = 1+x+y(x)+x*y(x),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = -1+{\mathrm e}^{\frac {x \left (2+x \right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 17
DSolve[{y'[x]== 1+x+y[x]+x*y[x],y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {1}{2} x (x+2)}-1 \\ \end{align*}