Internal problem ID [6]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-x \sqrt {x^{2}+9}=0} \end {gather*} With initial conditions \begin {align*} [y \left (-4\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 15
dsolve([diff(y(x),x) = x*(x^2+9)^(1/2),y(-4) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {x^{2}+9}\, x^{2}}{3}+3 \sqrt {x^{2}+9}-\frac {125}{3} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 20
DSolve[{y'[x] == x*(x^2+9)^(1/2),y[-4]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (\left (x^2+9\right )^{3/2}-125\right ) \\ \end{align*}