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

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

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

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

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

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

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

An integrating factor of the differential equation \[ (x^2+1)\frac{dy}{dx}+xy=x^3 \] is

If the general solution of \[ \frac{dy}{dx}=\frac{y^2}{xy-y^2-x^2} \] is \[ \tan^{-1}\left(\frac{y}{x}\right)=f(y)+C, \] then \(f(e^3)=\)

If \(a\) and \(b\) are respectively the order and degree of the differential equation \[ y^2(y'')^2+3x(y')^{1/3}+x^2y^2=\sin x, \] then

The differential equation of the family of circles passing through \((0,0)\) and having centre on \(x\)-axis is

If \[ \frac{a}{a_1}=\frac{b}{b_1}, \] then the substitution to be used to solve the differential equation \[ \frac{dy}{dx}=\frac{ax+by+c}{a_1x+b_1y+c_1} \] by using separation of variables is

For the differential equation \[ \frac{d^3y}{dx^3}=0, \] \(y=ax^2+bx+c\) is