65.5.9 problem 10.4 (ii)

Internal problem ID [13748]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number : 10.4 (ii)
Date solved : Tuesday, January 28, 2025 at 06:01:11 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x^{\prime }&=\frac {x^{2}+t \sqrt {t^{2}+x^{2}}}{x t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

dsolve(diff(x(t),t)=(x(t)^2+t*sqrt(t^2+x(t)^2))/(t*x(t)),x(t), singsol=all)
 

\[ \frac {t \ln \left (t \right )-c_{1} t -\sqrt {t^{2}+x \left (t \right )^{2}}}{t} = 0 \]

✓ Solution by Mathematica

Time used: 0.312 (sec). Leaf size: 54

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

\begin{align*} x(t)\to -t \sqrt {\log ^2(t)+2 c_1 \log (t)-1+c_1{}^2} \\ x(t)\to t \sqrt {\log ^2(t)+2 c_1 \log (t)-1+c_1{}^2} \\ \end{align*}