Internal problem ID [6149]
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]
\[ \boxed {y y^{\prime }=1+x} \] With initial conditions \begin {align*} [y \left (1\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 14
dsolve([diff(y(x),x)*y(x)=x+1,y(1) = 3],y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {x^{2}+2 x +6} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 17
DSolve[{y'[x]*y[x]==x+1,{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {x^2+2 x+6} \]