List of top Mathematics Questions on Differential equations asked in MET

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

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

The differential equation of the family \( y = a e^{x} + b x e^{x} + c x^{2} e^{x} \) is

The general solution of \( \frac{dy}{dx} = e^{x - y} \) is:

The general solution of \( \frac{dy}{dx} = e^{x - y} \) is:

The solution of the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) is: