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

The general solution of the differential equation \[ (4xy^2-2xy+2x^2y^2-x^2y)\,dx=dy \] is

If the differential equation of the family of curves given by \[ y=ae^x+b\cos x, \] where \(a\) and \(b\) are arbitrary constants, is \[ y_2(\cos x+\sin x)+y(\cos x-\sin x)=2y_1f(x), \] then \(f(x)=\)

Given that \[ \frac{dy}{dx}=ye^x \] and when \[ x=0,\quad y=e, \] then the value of \(y\) (\(y>0\)) when \(x=1\) is

If \(a\) and \(b\) are arbitrary constants, then the differential equation corresponding to the family of curves \[ ax^2+2hxy=1 \] is

The general solution of the differential equation \[ \frac{dy}{dx}=\frac{2xy-3y^2}{2x^2+3xy} \] is

The general solution of the differential equation \[ (x+y-1)\,dy=(x-y+1)\,dx \] is

Solve $\cos(x+y)dy=dx$

Solve $(1+y^2)+(x-e^{-\tan^{-1}y})\frac{dy}{dx}=0$

Eliminate constants from $y=A(x+B)^2$

Among the following differential equations, the equation having order 2 and degree 3 is:

The general solution of the differential equation \( \frac{dy}{dx} + y \tan x = - \tan x \log(\cos x) \) (\(0 < x < \pi/2\)) is:

Consider the differential equations \(\frac{dy}{dx}(x+y+1)=1\) and \(\frac{dx}{dy}=3y+2x^2\).
Which of the following is correct regarding these two differential equations?

The substitution required to reduce the differential equation \( \frac{dy}{dx}+\sin y \cos y \sin x = \sin 2x \cos^{2}y \) to a linear differential equation in z is

The differential equation among the following, whose general solution is \( y=A e^{5x}+B e^{-4x} \) is

The general solution of the differential equation \( \frac{dy}{dx}=x^{2}y(x+y+xy+1) \) is \( y = \)

At a point $P(x,y)$ on a curve $x=f(y)$, the x-intercept of the tangent is always equal to the y-coordinate of the point of contact, then $f(y)=$

If the degree of the differential equation $\left(\frac{d^{2}y}{dx^{2}}\right)^{3/2}+5\left(\frac{d^{2}y}{dx^{2}}\right)^{5/2}=7y$ is $m$ and its order is $n$, then $y=Ae^{mx}+Be^{nx}$ is solution of the differential equation

If $y=f(x)$ is a solution of $\frac{dy}{dx}=(y-kx)^{2}+K$ when $x=0$ and $y=1$, then $f(2)=$

The solution of the differential equation $x \frac{dy}{dx} + 2y = x^2$ is:

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

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:

The equation of the family of curves for which the length of the subnormal at any point \((x,y)\) is always a constant \(k\) is

If the differential equation obtained by eliminating \(A, B\) from \(y = (\sin^{-1}x)^2 + A \cos^{-1} x + B\) is \((a-x^2)y'' - xy' = b\), then \(\frac{b+a}{b-a} =\)

The general solution of \(\frac{d^2 y}{dx^2} = 0\) is