8.4.20 problem 20

Internal problem ID [723]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 20
Date solved : Monday, January 27, 2025 at 02:59:13 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 13

dsolve([diff(y(x),x) = 1+x+y(x)+x*y(x),y(0) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 17

DSolve[{D[y[x],x]== 1+x+y[x]+x*y[x],y[0]==0},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{\frac {1}{2} x (x+2)}-1 \]