60.9.30 problem 1885

Internal problem ID [11809]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1885
Date solved : Friday, March 14, 2025 at 02:58:24 AM
CAS classification : system_of_ODEs

\begin{align*} t \left (\frac {d}{d t}x \left (t \right )\right )-t \left (\frac {d}{d t}y \left (t \right )\right )-2 y \left (t \right )&=0\\ t \left (\frac {d^{2}}{d t^{2}}x \left (t \right )\right )+2 \frac {d}{d t}x \left (t \right )+t x \left (t \right )&=0 \end{align*}

✓ Maple. Time used: 0.134 (sec). Leaf size: 46

ode:=[t*diff(x(t),t)-t*diff(y(t),t)-2*y(t) = 0, t*diff(diff(x(t),t),t)+2*diff(x(t),t)+t*x(t) = 0]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= \frac {c_{2} \sin \left (t \right )+c_3 \cos \left (t \right )}{t} \\ y \left (t \right ) &= \frac {\sin \left (t \right ) c_{2} t +\cos \left (t \right ) c_3 t -2 c_3 \sin \left (t \right )+2 c_{2} \cos \left (t \right )+c_{1}}{t^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 54

ode={t*D[x[t],t]-t*D[y[t],t]-2*y[t]==0,t*D[x[t],{t,2}]+2*D[x[t],t]+t*x[t]==0}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to \frac {c_2 \cos (t)+c_3 \sin (t)}{t} \\ y(t)\to \frac {c_2 t \cos (t)+2 c_3 \cos (t)-2 c_2 \sin (t)+c_3 t \sin (t)+c_1}{t^2} \\ \end{align*}

✗ Sympy

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

Timed Out