Teaching CSIR NET Mock Test Series Mathematical Science Ordinary Differential Equations System of ODE
If x1 = x1(t) , x2 = x2(t) is the solution of the initial value problem
\(\rm e^{-t}\frac{dx_1}{dt}=-x_1+x_2, \)
\(\rm e^{-t}\frac{dx_2}{dt}=-x_1-x_2, \)
x1(0) = 1, x2(0) = 0 and r(t) = \(\rm \sqrt{x_1^2(t)+x_2^2(t)} \), then which of the following statements are true?
1
r(t) → 0 as t → +∞
2
r(ln 2) = e-1
3
r(ln 2) = 2e-1
4
r(t)et → 0 as t → +∞