69.1.14 problem 14

Internal problem ID [14167]
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
Date solved : Tuesday, January 28, 2025 at 06:18:31 AM
CAS classification : [_separable]

\begin{align*} z-\left (-a^{2}+t^{2}\right ) z^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(z(t)-(t^2-a^2)*diff(z(t),t)=0,z(t), singsol=all)
 

\[ z = c_{1} \left (t -a \right )^{\frac {1}{2 a}} \left (t +a \right )^{-\frac {1}{2 a}} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 34

DSolve[z[t]-(t^2-a^2)*D[z[t],t]==0,z[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} z(t)\to c_1 \exp \left (\int _1^t\frac {1}{K[1]^2-a^2}dK[1]\right ) \\ z(t)\to 0 \\ \end{align*}