Differential Equations - General Aptitude - General Aptitude (GA) Previous Year Questions

A separately excited DC generator has an armature resistance of \(0.1\Omega\) and negligible armature inductance. At rated field current and rated rotor speed, its open-circuit voltage is \(200\text{ V}\). When this generator is operated at half the rated speed, with half the rated field current, an uncharged \(1000\ \mu\text{F}\) capacitor is suddenly connected across the armature terminals. Assume that the speed remains unchanged during the transient. At what time (in microsecond) after the capacitor is connected will the voltage across it reach \(25\text{ V}\)?

A solution of the ordinary differential equation \(\frac{d^2y}{dt^2} + 5\frac{dy}{dt} + 6y = 0\) is such that \(y(0) = 2\) and \(y(1) = -\frac{1-3e}{e^3}\). The value of \(\frac{dy}{dt}(0)\) is ______.

A differential equation \(\frac{di}{dt} - 0.2i = 0\) is applicable over -10 < t < 10. If i(4) = 10, then i(-5) is ______.

The solution of the differential equation, for \(t > 0\), \(y''(t) + 2y'(t) + y(t) = 0\) with initial conditions \(y(0) = 0\) and \(y'(0) = 1\), is (\(u(t)\) denotes the unit step function),