Internal problem ID [12143]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {x^{\prime }-\frac {x}{t}-\frac {x^{2}}{t^{3}}=0} \] With initial conditions \begin {align*} [x \left (2\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 7
dsolve([diff(x(t),t)=x(t)/t+x(t)^2/t^3,x(2) = 4],x(t), singsol=all)
\[ x \left (t \right ) = t^{2} \]
✓ Solution by Mathematica
Time used: 0.264 (sec). Leaf size: 8
DSolve[{x'[t]==x[t]/t+x[t]^2/t^3,{x[2]==4}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to t^2 \]