63.1.7 problem 7

Internal problem ID [12952]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.1 First order equations. Exercises page 10
Problem number : 7
Date solved : Wednesday, March 05, 2025 at 08:54:42 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 9

ode:=2*t*diff(x(t),t) = x(t); 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = c_{1} \sqrt {t} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 18

ode=2*t*D[x[t],t]==x[t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to c_1 \sqrt {t} \\ x(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.133 (sec). Leaf size: 8

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

\[ x{\left (t \right )} = C_{1} \sqrt {t} \]