79.1.16 problem 3 (iv)

Internal problem ID [18503]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 3 (iv)
Date solved : Tuesday, January 28, 2025 at 11:51:15 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 19

dsolve((t^2-x(t)^2)*diff(x(t),t)=t*x(t),x(t), singsol=all)
 

\[ x = \sqrt {-\frac {1}{\operatorname {LambertW}\left (-c_{1} t^{2}\right )}}\, t \]

✓ Solution by Mathematica

Time used: 7.380 (sec). Leaf size: 56

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

\begin{align*} x(t)\to -\frac {i t}{\sqrt {W\left (-e^{-2 c_1} t^2\right )}} \\ x(t)\to \frac {i t}{\sqrt {W\left (-e^{-2 c_1} t^2\right )}} \\ x(t)\to 0 \\ \end{align*}