Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Ordinary Differential Equations System of ODE
Consider the linear system y' = Ay + h where
\(A=\left(\begin{array}{cc} 1 & 1 \\ 4 & -2 \end{array}\right) \) and \( h=\left(\begin{array}{l} 2 t+3 \\ 3t+2 \end{array}\right)\).
Suppose y(t) is a solution such that
\(\displaystyle \lim _{t \rightarrow \infty} \frac{y(t)}{t}=d \in \mathbb{R}^2\)
What is the value of d?
1
\(\left(\begin{array}{c} 1 \\ 1 \end{array}\right)\)
2
\(\left(\begin{array}{c} -1 \\ 4 \end{array}\right)\)
3
\(\left(\begin{array}{c} -67 / 12 \\ 17 / 12 \end{array}\right)\)
4
\(\left(\begin{array}{l} -7 / 6 \\ -5 / 6 \end{array}\right)\)
5
Question Not Attempted