List of top Mathematics & Statistics Questions on Differential Equations

The population of a town grows at a rate proportional to its size. If it grows from 40,000 to 60,000 in 40 years, what will it be in another 20 years?
Write the order of the differential equation \[ \sqrt{1 + \left( \frac{dy}{dx} \right)^2} = \left( \frac{d^2y}{dx^2} \right)^{\frac{3}{2}}. \]
Find the differential equation by eliminating arbitrary constants from the relation \( y = Ae^{3x} + Be^{-3x} \).
Solve the following differential equation \( (x^2 - yx^2)dy + (y^2 + xy^2)dx = 0 \).
The order and degree of the differential equation \( \left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = a^x \) are ............. respectively.
The integrating factor of the differential equation \( \frac{dy}{dx} + \frac{y}{x} = x^3 - 3 \) is:
The differential equation obtained by eliminating arbitrary constants from \( bx + ay = ab \) is \( \frac{d^2y}{dx^2} = 0 \).
Solve \( x + y \frac{dy}{dx} = \sec (x^2 + y^2) \)
Form the differential equation of all lines which make intercept 3 on x-axis.
Solve the differential equation \( y \frac{dy}{dx} + x = 0 \)
Write the degree of differential equation \( (y''')^4 + 3(y'') + 3xy + 5y = 0 \)