8.1.6 problem 6

Internal problem ID [656]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.2. Integrals as general and particular solutions. Page 16
Problem number : 6
Date solved : Monday, January 27, 2025 at 02:56:45 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*(x^2+9)^(1/2),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: 0.006 (sec). Leaf size: 20

DSolve[{D[y[x],x] == x*(x^2+9)^(1/2),y[-4]==0},y[x],x,IncludeSingularSolutions -> True]
 

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