8.3.16 problem 17

Internal problem ID [692]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 17
Date solved : Monday, January 27, 2025 at 02:58:09 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=1+x +y+y x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(y(x),x) = 1+x+y(x)+x*y(x),y(x), singsol=all)
 

\[ y = -1+{\mathrm e}^{\frac {x \left (x +2\right )}{2}} c_1 \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 25

DSolve[D[y[x],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*}