List of top Mathematics Foundation Questions on Differential Equations asked in GATE ES

$f(x) = x^3 – 4.5x^2 - 12x$ has a local maximum at x = ___________(an integer value) in the range x = − 2 to + 2

Consider the equation - $\farc{dy}{dx}- x^2 + e^x = 0;$ with y =1 at x = 0.
The value of y at x = 1 is _________. (rounded off to 2 decimal places).
Take the value of e (base of natural logarithm) as 2.7.

Which one is the solution y(x) for the following ordinary differential equation and the specified boundary conditionmys?
\(\frac{d^2y}{dx^2} -3 \frac{dy}{dx}+2y = 2e ^{-x}; y(0) =2; (\frac{dy}{dx}_{x=0})=1\)