76.10.21 problem 22 (iii)

Internal problem ID [17543]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 3. Systems of two first order equations. Section 3.6 (A brief introduction to nonlinear systems). Problems at page 195
Problem number : 22 (iii)
Date solved : Tuesday, January 28, 2025 at 10:40:05 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=\frac {x \sqrt {6 x-9}}{3} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.443 (sec). Leaf size: 16

dsolve([diff(x(t),t)=1/3*x(t)*sqrt(6*x(t)-9),x(0) = 3],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {3 \sec \left (\frac {\pi }{4}+\frac {t}{2}\right )^{2}}{2} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 21

DSolve[{D[x[t],t]==1/3*x[t]*Sqrt[6*x[t]-9],{x[0]==3}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {3}{2} \sec ^2\left (\frac {1}{4} (2 t+\pi )\right ) \]