List of top Engineering Mathematics Questions on Calculus asked in GATE CE

A function f(x) is defined on the interval with values in R. It satisfies \( \int_0^2 f(x)[x-f(x)]dx = \frac{2}{3} \). Find the value of f(1).}

Find the order and degree of the following differential equation: \[ \frac{d^3 y}{dx^3} + \frac{d^2 y}{dx^2} + \frac{dy}{dx} + y = 0 \]

Solve the second-order differential equation: \[ y'' + 0.8 y' + 0.16 y = 0, \quad y(0) = 3, \quad y'(0) = 4.5 \]