7.4.20 problem 20

Internal problem ID [92]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 20
Date solved : Friday, February 07, 2025 at 07:49:04 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 17

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

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