69.1.27 problem 44

Internal problem ID [14101]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 44
Date solved : Wednesday, March 05, 2025 at 10:33:02 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} 2 \sqrt {s t}-s+t s^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 18

ode:=2*(s(t)*t)^(1/2)-s(t)+t*diff(s(t),t) = 0; 
dsolve(ode,s(t), singsol=all);
 

\[ \frac {s}{\sqrt {s t}}+\ln \left (t \right )-c_{1} = 0 \]

✓ Mathematica. Time used: 0.176 (sec). Leaf size: 19

ode=(2*Sqrt[s[t]*t]-s[t])+t*D[s[t],t]==0; 
ic={}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\[ s(t)\to \frac {1}{4} t (-2 \log (t)+c_1){}^2 \]

✓ Sympy. Time used: 0.479 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(t*Derivative(s(t), t) + 2*sqrt(t*s(t)) - s(t),0) 
ics = {} 
dsolve(ode,func=s(t),ics=ics)
 

\[ s{\left (t \right )} = C_{1}^{2} t + t \log {\left (t \right )}^{2} - \log {\left (t^{2 C_{1} t} \right )} \]