7.1.6 problem 6

Internal problem ID [6]
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 1.2. Problems at page 17
Problem number : 6
Date solved : Friday, February 07, 2025 at 08:11:45 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=x \sqrt {x^{2}+9} \end{align*}

With initial conditions

\begin{align*} y \left (-4\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 27

dsolve([diff(y(x),x)=x*sqrt(x^2+9),y(-4) = 0],y(x), singsol=all)
 

\[ y = \frac {x^{2} \sqrt {x^{2}+9}}{3}+3 \sqrt {x^{2}+9}-\frac {125}{3} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 20

DSolve[{D[y[x],x]==x*Sqrt[x^2+9],{y[-4]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} \left (\left (x^2+9\right )^{3/2}-125\right ) \]