60.9.20 problem 1875

Internal problem ID [11799]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1875
Date solved : Friday, March 14, 2025 at 02:58:19 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+\left (a x \left (t \right )+b y \left (t \right )\right ) f \left (t \right )&=g \left (t \right )\\ \frac {d}{d t}y \left (t \right )+\left (c x \left (t \right )+d y \left (t \right )\right ) f \left (t \right )&=h \left (t \right ) \end{align*}

✓ Maple. Time used: 3.227 (sec). Leaf size: 3921

ode:=[diff(x(t),t)+(a*x(t)+b*y(t))*f(t) = g(t), diff(y(t),t)+(c*x(t)+d*y(t))*f(t) = h(t)]; 
dsolve(ode);
 

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Mathematica. Time used: 0.737 (sec). Leaf size: 3095

ode={D[x[t],t]+(a*x[t]+b*y[t])*f[t]==g[t],D[y[t],t]+(c*x[t]+d*y[t])*f[t]==h[t]}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

Too large to display

✓ Sympy. Time used: 37.585 (sec). Leaf size: 110390

from sympy import * 
t = symbols("t") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
d = symbols("d") 
x = Function("x") 
y = Function("y") 
ode=[Eq((a*x(t) + b*y(t))*f(t) - g(t) + Derivative(x(t), t),0),Eq((c*x(t) + d*y(t))*f(t) - h(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \text {Too large to display} \]