List of top Mathematics Questions on Differential equations asked in MET

Given \(\frac{dy}{dx} + 2y\tan x = \sin x\), \(y=0\) at \(x=\frac{\pi}{3}\). If maximum value of \(y\) is \(1/k\), find \(k\).

The differential equation of all circles which pass through the origin and whose centres lie on Y-axis is:

The differential equation of all circles passing through the origin and having their centre on the X-axis is

Differential equation of family \(y=a\cos \mu x + b\sin \mu x\) is

Let \(f(x)\) be differentiable on the interval \((0,\infty)\) such that \(f(1)=1\) and \[ \lim_{t \to x} \frac{t^2 f(x) - x^2 f(t)}{t - x} = 1 \quad \text{for each } x>0. \] Then, \(f(x)\) is equal to

Solution of the equation \[ \cos^2 x \frac{dy}{dx} - (\tan 2x)\,y = \cos^4 x,\quad |x|<\frac{\pi}{4}, \] where \(y\!\left(\frac{\pi}{6}\right)=\frac{3\sqrt{3}}{8}\), is given by:

The equation of the curve through \((1,0)\), whose slope is \(\frac{y-1}{x^2+x}\), is:

The solution of differential equation \(y\log x - y\,dx = x\,dy\) is

The solution of the differential equation \[ \sqrt{a+x}\,\frac{dy}{dx} + xy = 0 \] is

The general solution of the differential equation \(\frac{dy}{dx} = y\tan x - y^2\sec x\) is:

The equation of the curve passing through the origin and satisfying $\dfrac{dy}{dx} = (x - y)^{2}$ is

The differential equation of the family of curves $y = a\cos\mu x + b\sin\mu x$, where $a$ and $b$ are arbitrary constants, is

If $x(1+y^{2})\,dx + y(1+x^{2})\,dy = 0$ and $y(0) = 1$, then $x^{2}y^{2} + x^{2} + y^{2}$ equals

By eliminating the arbitrary constants $A$ and $B$ from $y = Ax^{2} + Bx$, the differential equation obtained is

The general solution of $x\sqrt{1+y^{2}}\,dx + y\sqrt{1+x^{2}}\,dy = 0$ is

The degree of the differential equation $5\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^3y}{dx^3}\right)^2 = x\left(\frac{d^2y}{dx^2}\right)^5$ is

The differential equation of the family of lines passing through the origin is

The solution of the equation $(2y-1)dx + (2x-3)dy = 0$ is

If \(f(x)\) is a non-negative continuous function for all \(x \ge 1\) such that \(f'(x) \le p f(x)\), where \(p > 0\) and \(f(1) = 0\), then \([f(\sqrt{e}) + f(\sqrt{\pi})]\) is equal to

The differential equation of the family of curves \(y = Ae^{3x} + Be^{5x}\), where \(A\) and \(B\) are arbitrary constants, is

The solution of the differential equation \(\frac{dy}{dx} = \sin(x + y) \tan(x + y) - 1\) is

The degree of the differential equation \( x = \frac{dy}{dx} + \frac{1}{2!} \left(\frac{dy}{dx}\right)^2 + \frac{1}{3!} \left(\frac{dy}{dx}\right)^3 + \cdots \) is:

If \(y^{1/m} + y^{-1/m} = 2x\), then \((x^2 - 1)y'' + xy'\) is equal to

\((\sim p \wedge q)\) is logically equivalent to

If \(m\) parallel lines in a plane are intersected by a family of \(n\) parallel lines, then the number of parallelograms that can be formed is