Internal problem ID [10375]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }-6 t \left (x-1\right )^{\frac {2}{3}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(x(t),t)=6*t*(x(t)-1)^(2/3),x(t), singsol=all)
\[ c_{1} +t^{2}-\left (x \left (t \right )-1\right )^{\frac {1}{3}} = 0 \]
✓ Solution by Mathematica
Time used: 0.195 (sec). Leaf size: 26
DSolve[x'[t]==6*t*(x[t]-1)^(2/3),x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 1+\frac {1}{27} \left (3 t^2+c_1\right ){}^3 \\ x(t)\to 1 \\ \end{align*}