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

The solution of the differential equation $x \frac{dy}{dx} + 2y = x^2$ is:
The general solution of the differential equation $\frac{dy}{dx} + y \cot x = 2 \cos x$ is:
The integrating factor of the differential equation $(1 + x^2) \frac{dy}{dx} + 2xy = \cos x$ is:
If the slope of the tangent drawn at any point \((x, y)\) on a curve is \(x + y\), then the equation of that curve is
The solution of the differential equation \( x^2 (y + 1) \frac{dy}{dx} + y^2 (x + 1) = 0 \), when \( y(1) = 2 \), is
The general solution of the differential equation \( \frac{dy}{dx} = \frac{2x + y - 3}{2y - x + 3} \) is
If $$ y = A t^2 + \frac{B}{t} \quad (A, B \text{ constants}) $$ is a general solution of the differential equation $$ f(t) y'' + g(t) y' + h(t) y = 0, $$ then find the relation between $ g(t), f(t), h(t) $.
If \( x \log_{10} x \frac{dy}{dx} + y = 2 \log_{10} x \) and \( y(e) = 0 \), then \( y(e^2) = \)
Find the general solution of: $$ (2x - y)^2 dy - 2(2x - y)^2 dx - 2 dx = 0 $$
Find the general solution of the differential equation: $$ x \log x \, dy = (x \log x - y) dx $$
The general solution of the differential equation \( \frac{dy}{dx} + 2y = e^{-x} \) is:
If $ a $ and $ b $ are the roots of the equation $ 4x^2 - 12x + 11 = 0 $, find the value of $ a^2 + b^2 $.

The general solution of the differential equation $$ (y^2 + x + 1) \, dy = (y + 1) \, dx $$ is: 

The differential equation formed by eliminating arbitrary constants \( A \) and \( B \) from the equation \[ y = A \cos 3x + B \sin 3x \] is:
If \[ \cos x \frac{dy}{dx} - y \sin x = 6x, \quad (0 < x < \frac{\pi}{2}) \quad \text{and} \quad y(\frac{\pi}{3}) = 0, \quad \text{then} \quad y(\frac{\pi}{6}) = \]

The general solution of the differential equation \[ (x + y)y \,dx + (y - x)x \,dy = 0 \] is: 

The solution of the differential equation \[ \frac{dy}{dx} = \frac{y + x \tan \left( \frac{y}{x} \right)}{x}. \] \[ \sin\frac{y}{x} = \]

The sum of the order and degree of the differential equation: \[ \frac{d^y}{dx^t} = c + \left( \frac{d^y}{dx^t} \right)^{\frac{3}{2}} \] is: 

If $\log y$ is an integrating factor of $\frac{dx}{dy}+P(y)x=Q(y)$, then $P(y)=$
If $X=x+h, Y=y+k$ transforms $\frac{dy}{dx} = \frac{2x+3y-7}{3x+2y-8}$ to a homogeneous differential equation, then $(h,k)=$
Which one of the following is a linear differential equation?
Let $ a $ and $ b $ be arbitrary constants and $ C $ be a fixed constant. If $ y = ae^{2x} + bxe^{2x} + C $ is the general solution of a differential equation, then the order of that differential equation is:
The differential equation \[ y^2 \, dx + (3xy - 1) \, dy = 0 \] is:
If the solution of \(\dfrac{dy}{dx}=\dfrac{y^3\cos\sqrt{x}}{\sqrt{x}e^{1/y^2}}\), \(y(0)=1\), is \(\dfrac{1}{y^2}=\log_e(f(x))\), then \(f(x)=\)
Suppose that \(f(x,y)\) and \(g(x,y)\) are homogeneous functions of same order. If \(x=Vy\) reduces the equation \(\dfrac{dy}{dx}=\dfrac{f(x,y)}{g(x,y)}\) to the form \(\dfrac{dV}{dy}=\dfrac{1}{y}(F(V))\), then \(F(V)=\)