Internal problem ID [5396]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page
12
Problem number: 2(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } y-1-x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 14
dsolve([diff(y(x),x)*y(x)=x+1,y(1) = 3],y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x^{2}+2 x +6} \]
✓ Solution by Mathematica
Time used: 0.141 (sec). Leaf size: 16
DSolve[{y'[x]*y[x]==x+1,{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x (x+2)+6} \\ \end{align*}