Internal problem ID [11398]
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: 10(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {T^{\prime }-2 a t \left (T^{2}-a^{2}\right )=0} \] With initial conditions \begin {align*} [T \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.687 (sec). Leaf size: 31
dsolve([diff(T(t),t)=2*a*t*(T(t)^2-a^2),T(0) = 0],T(t), singsol=all)
\[ T \left (t \right ) = -\frac {a \left ({\mathrm e}^{2 t^{2} a^{2}}-1\right )}{{\mathrm e}^{2 t^{2} a^{2}}+1} \]
✓ Solution by Mathematica
Time used: 3.308 (sec). Leaf size: 16
DSolve[{T'[t]==2*a*t*(T[t]^2-a^2),{T[0]==0}},T[t],t,IncludeSingularSolutions -> True]
\[ T(t)\to -a \tanh \left (a^2 t^2\right ) \]