Internal problem ID [12111]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {z-\left (-a^{2}+t^{2}\right ) z^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(z(t)-(t^2-a^2)*diff(z(t),t)=0,z(t), singsol=all)
\[ z \left (t \right ) = c_{1} \left (-a +t \right )^{\frac {1}{2 a}} \left (a +t \right )^{-\frac {1}{2 a}} \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 26
DSolve[z[t]-(t^2-a^2)*z'[t]==0,z[t],t,IncludeSingularSolutions -> True]
\begin{align*} z(t)\to c_1 e^{-\frac {\text {arctanh}\left (\frac {t}{a}\right )}{a}} z(t)\to 0 \end{align*}