List of top Mathematics for Economy Questions on Differential Equations asked in IIT JAM EN

Let $f ∶ R^2 → R$ be a function defined as
$f(x,y) =\begin{cases}\frac{x^2y}{x^4 + Y^2} & if (x, y) \neq (0, 0)\\ 0 & if (x, y) = (0, 0)\end{cases} $ Then, which of the following is/are CORRECT?

The differential equation satisfied by circles with radius 3 and center lying on the Y-axis is

The solution of the differential equation
$ xy 𝑑𝑥 − (x^2 + y^2) 𝑑y = 0, y(0) = 1$ is

Let 𝑦 = 𝑦(𝑥) be a solution curve of the differential equation
\(𝑥 \frac{𝑑𝑦}{d𝑥} = 𝑦 \) ln ( \(\frac{y}{x}\) ) , 𝑦 > 𝑥 > 0. 
If 𝑦(1) = 𝑒 ² and 𝑦(2) = 𝛼, then the value of \(\frac{𝑑𝑦}{𝑑𝑥}\) at (2, 𝛼) is equal to

Let a second order difference equation be
\(y_{n+2} + 4y_n = 4y_{n+1}, \, n=2,3,4,......, \,\, y_0=1, y_1=4\)
Then the general solution is

Let the function \(f: R^2⇢R\)  be \(f(x, y) = \frac{xy^2}{ x^3+  2xy + y^3}\,\,  f(0, 0) = 0.\) Then

Let ƒ be defined by $f(x) = |x| + |cos({\frac{\pi }{2} - x }), x \, \, \epsilon \, \,(-\frac{\pi }{2},\frac{\pi }{2}).$ Then

Let the system of equations be αu+w=0, u+αν =0, v+αw=0, where a ∈ ℜ. Then the system has infinite solutions if a =_____ (in integer).