66.1.32 problem Problem 46

Internal problem ID [13879]
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
Date solved : Tuesday, January 28, 2025 at 06:07:05 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} x^{\prime }&=\frac {x}{t}+\frac {x^{2}}{t^{3}} \end{align*}

With initial conditions

\begin{align*} x \left (2\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.028 (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: 0.175 (sec). Leaf size: 8

DSolve[{D[x[t],t]==x[t]/t+x[t]^2/t^3,{x[2]==4}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to t^2 \]