List of top Statistical Science Questions on Differential Equations asked in ICAR AIEEA (PG)

If the function \(f(x,y)\) has mixed second order partial derivatives \(f_{xy}\) and \(f_{yx}\) that are continuous in an open disk containing \((x_0,y_0)\), then:

The solution of the differential equation \(\frac{d^2x}{dt^2}+6\frac{dx}{dt}+9x=0\) is given by:

The solution of the differential equation $\cos(x+y)dx + [3y^2 + 2y + \cos(x+y)]dy = 0$ is given by :

The solution of the differential equation \(xy^{\prime\prime}+y^{\prime}=4x\) is given by:

If \(\theta=t^n e^{-\frac{r^2}{4t}}\), then the value of \(n\) that will make \(\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial \theta}{\partial r}\right)=\frac{\partial \theta}{\partial t}\) is given by:

The general solution of the differential equation \(\frac{dy}{dx} = \frac{x^2}{y^2}\) is :

Find the order of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^3 + y^4 = 0\)

If \(\theta=t^n e^{-\frac{r^2}{4t}}\), then the value of \(n\) that will make \(\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial \theta}{\partial r}\right)=\frac{\partial \theta}{\partial t}\) is given by:

The solution of the differential equation \(\frac{d^2x}{dt^2}+6\frac{dx}{dt}+9x=0\) is given by:

The solution of the differential equation $\cos(x+y)dx + [3y^2 + 2y + \cos(x+y)]dy = 0$ is given by :

The solution of the differential equation $\text{xy'' + \text{y}' = 4\text{x}$ is given by :}

Integrating factor for the differential equation \((x^2 + y^2 + x) \, dx + xy \, dy = 0\) is:

Number of first order equations in a system equivalent to the equation \(x''' + 3x'' + 2x' - 5x = \sin 2t\) is:

For the system \(x' = y; \, y' = -x\), the solution curve has the form:

A solution to the difference equation \(u_{x+3} - 3u_{x+1} - 2u_x = 0\) is of the form:

A solution to the differential equation \(\left(y - x \frac{dy}{dx}\right) = a \left(y^2 + \frac{dy}{dx}\right)\) is:

Which of the following equations is exact?

Solution of the differential equation \(x \sin \frac{y}{x} \, dy = \left( y \sin \frac{y}{x} - x \right) dx\) is:

For the differential equation \(x^{\alpha} y^{\beta} (m y \, dx + n x \, dy) = 0\), the integrating factor, for any value of \(k\) is: