Internal problem ID [12109]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (t^{2}+t^{2} x\right ) x^{\prime }+x^{2}+t x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve((t^2+x(t)*t^2)*diff(x(t),t)+x(t)^2+t*x(t)^2=0,x(t), singsol=all)
\[ x \left (t \right ) = \frac {1}{\operatorname {LambertW}\left (t c_{1} {\mathrm e}^{-\frac {1}{t}}\right )} \]
✓ Solution by Mathematica
Time used: 5.02 (sec). Leaf size: 27
DSolve[(t^2+x[t]*t^2)*x'[t]+x[t]^2+t*x[t]^2==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{W\left (t e^{-\frac {1}{t}-c_1}\right )} x(t)\to 0 \end{align*}