66.1.32 problem Problem 46

Internal problem ID [13808]
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 : Monday, March 31, 2025 at 08:13:31 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*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 7

ode:=diff(x(t),t) = x(t)/t+x(t)^2/t^3; 
ic:=x(2) = 4; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = t^{2} \]

✓ Mathematica. Time used: 0.175 (sec). Leaf size: 8

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

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

✓ Sympy. Time used: 0.211 (sec). Leaf size: 5

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), t) - x(t)/t - x(t)**2/t**3,0) 
ics = {x(2): 4} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = t^{2} \]