List of top Mathematics Questions on Differential equations asked in VITEEE

The order and degree of the differential equation \[ \left( 1 + 4 \frac{dy}{dx} \right)^{2/3} = 4 \frac{d^2 y}{dx^2} \] are respectively:

The solution of the differential equation \[ \frac{dy}{dx} = (4x + y + 1)^2 \] is:

The degree of differential equation of all curves having normal of constant length \(c\) is

The solution of the differential equation
\[ \frac{dy}{dx}=\sin(x+y)\tan(x+y)-1 \] is

Let \(y\) be the number of people in a village at time \(t\). Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increases in time. Then the population of the village at any fixed time \(t\) is given by

The differential equation of all straight lines touching the circle \(x^2+y^2=a^2\) is

The differential equation \(\left|\frac{dy}{dx}\right|+|y|+3=0\) admits

Solution of the differential equation \(xdy-ydx-\sqrt{x^2+y^2}\,dx=0\) is

Let $y$ be the number of people in a village at time $t$. Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increases in time. Then the population of the village at any fixed time $t$ is given by

If \( x \sin \left( \frac{y}{x} \right) \, dy = \sin \left( \frac{y}{x} \right) - x \, dx \) and \( y(1) = \frac{\pi}{2} \), then the value of \( \cos \left( \frac{y}{x} \right) \) is

The differential equation of the system of all circles of radius r in the XY plane is

The general solution of the differential equation \[ \frac{d^2 y}{dx^2} + \frac{dy}{dx} + y = 2e^{3x} \] is given by

The solution of the differential equation \[ \frac{dy}{dx}(x - y^3) = 0 \] is

The differential equation that represents all parabolas each of which has a latus rectum \( 4a \) and whose axes are parallel to the x-axis is:

The solution of \( x \sec \left( \frac{x}{y} \right) - y \, dx + x \, dy = 0 \) is:

The particular integral of \( \frac{d^2 y}{dx^2} + 2y = x^2 \) is:

The solution of \( D^2 + 16y = \cos 4x \) is:

Which of the following is a tautology?

Let a, b be elements of the group G. Assume that A has order 5 and a3b = ba3, then G is

Let f(x) = | |x| – 1|, then the point where f(x)is not differentiable, is / are?

If z1, z2, z3 are the vertices of the equilateral triangle and the z0 be its orthocentre, such that z12+z22+z32 = Kz02, then K equals

Max value of x+3y subject to conditions x+y≤4, 0≤x≤3 & 0≤y≤2 is?