Internal problem ID [12012]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x^{\prime }-\frac {x^{2}+t \sqrt {x^{2}+t^{2}}}{x t}=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.512 (sec). Leaf size: 54
DSolve[x'[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*}