63.4.26 problem 15

Internal problem ID [13069]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 04:51:12 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(diff(x(t),t)=6*t*(x(t)-1)^(2/3),x(t), singsol=all)
 

\[ c_{1} +t^{2}-\left (x \left (t \right )-1\right )^{{1}/{3}} = 0 \]

✓ Solution by Mathematica

Time used: 0.177 (sec). Leaf size: 40

DSolve[D[x[t],t]==6*t*(x[t]-1)^(2/3),x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to t^6+c_1 t^4+\frac {c_1{}^2 t^2}{3}+1+\frac {c_1{}^3}{27} \\ x(t)\to 1 \\ \end{align*}