60.9.33 problem 1888

Internal problem ID [11812]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1888
Date solved : Sunday, March 30, 2025 at 09:15:52 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d^{2}}{d t^{2}}x \left (t \right )&=a_{1} x \left (t \right )+b_{1} y \left (t \right )+c_{1}\\ \frac {d^{2}}{d t^{2}}y \left (t \right )&=a_{2} x \left (t \right )+b_{2} y \left (t \right )+c_{2} \end{align*}

✓ Maple. Time used: 0.237 (sec). Leaf size: 651

ode:=[diff(diff(x(t),t),t) = a__1*x(t)+b__1*y(t)+c__1, diff(diff(y(t),t),t) = a__2*x(t)+b__2*y(t)+c__2]; 
dsolve(ode);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 19.813 (sec). Leaf size: 19318

ode={D[x[t],{t,2}]==a1*x[t]+b1*y[t]+c1,D[y[t],{t,2}]==a2*x[t]+b2*y[t]+c2}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
t = symbols("t") 
a__1 = symbols("a__1") 
a__2 = symbols("a__2") 
b__1 = symbols("b__1") 
b__2 = symbols("b__2") 
c__1 = symbols("c__1") 
c__2 = symbols("c__2") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-a__1*x(t) - b__1*y(t) - c__1 + Derivative(x(t), (t, 2)),0),Eq(-a__2*x(t) - b__2*y(t) - c__2 + Derivative(y(t), (t, 2)),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

Timed Out