50.2.11 problem 2(a)

Internal problem ID [7817]
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)
Date solved : Monday, January 27, 2025 at 03:24:00 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.047 (sec). Leaf size: 14

dsolve([diff(y(x),x)*y(x)=x+1,y(1) = 3],y(x), singsol=all)
 

\[ y = \sqrt {x^{2}+2 x +6} \]

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 17

DSolve[{D[y[x],x]*y[x]==x+1,{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x^2+2 x+6} \]