List of top Mathematics Questions on Differential equations asked in AP EAMCET

Find the general solution of the differential equation \( ( \sin y \cos^2 y - x \sec^2 y ) dy = (\tan y) dx \).
The solution of the differential equation \[ x dy - y dx = \sqrt{x^2 + y^2} dx \] when \( y(\sqrt{3}) = 1 \) is:
Among the options given below, from which option a differential equation of order two can be formed?
If the length of the sub-tangent at any point P on a curve is proportional to the abscissa of the point P, then the equation of that curve is (C is an arbitrary constant):
The general solution of the differential equation: $$ x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx. $$ 
The general solution of the differential equation: \[ (1 + \tan y) (dx - dy) + 2x \, dy = 0. \]
The sum of the order and degree of the differential equation: \[ x \left( \frac{d^2 y}{dx^2} \right)^{1/2} = \left( 1 + \frac{dy}{dx} \right)^{4/3} \] is:
The differential equation of the family of hyperbolas having their centers at origin and their axes along the coordinate axes is:
Find the differential equation representing the family of circles having their centers on the Y-axis. Given that \( y_1 = \frac{dy}{dx} \) and \( y_2 = \frac{d^2y}{dx^2} \).
Find the general solution of the differential equation: $$ (xy + y^2)dx - (x^2 - 2xy)dy = 0. $$ is 
If the differential equation $$ x \, dy + (y + y^2 x) \, dx = 0 $$ with condition \( y = 1 \) at \( x = 1 \), then the solution is: 
The difference of the order and degree of the differential equation \[ \left(\frac{d^2y}{dx^2} \right)^{-7/2} - \left(\frac{d^3y}{dx^3} \right)^2 - \left(\frac{d^2y}{dx^2} \right)^{-5/2} - \left(\frac{d^4y}{dx^4} \right) = 0 \]
Find the general solution of the differential equation \( (x - y -1) dy = (x + y + 1) dx \).
The differential equation for which \( ax + by = 1 \) is the general solution is:
The solution of the differential equation \( e^x y dx + e^x dy + xdx = 0 \) is:
At any point \((x,y)\) on a curve if the length of the subnormal is \((x-1)\) and the curve passes through \((1,2)\), then the curve is a conic. A vertex of the curve is
\(y=Ae^x+Be^{-2x}\) satisfies which of the following differential equations?
If the solution of \[ \frac{dy}{dx}-y\log_e0.5=0,\quad y(0)=1, \] and \(y(x)\to k\), as \(x\to\infty\) then \(k=\)