Form the differential equation by eliminating α and β from (x − α)² + (y − β)² = r²

Find the differential equation of the family of all straight lines passing through the origin.

Form the differential equation that represents all parabolas each of which has a latus rectum 4a and whose axes are parallel to the x axis.

Find the differential equation of all circles passing through the origin and having their centers on the y axis.

Find the differential equation of the family of parabola with foci at the origin and axis along the x-axis.

Find the differential equation of the family of curves y = e^x (acos x + bsin x) where a and b are arbitrary constants.

Find the differential equation of the family of curves \(y=\frac { a }{ x } +b\) where a and b are arbitrary constants

Find the differential equation corresponding to y = ae^4x + be^−x where a, b are arbitrary constants.

Solve \(\frac { dy }{ dx } \) = e^x−y+ x²e^{− y}

Solve sec²x tan y dx + sec²y tan x dy = 0

Solve \(y d x-x d y-3 x^{2} y^{2} e^{x^{3}} d x=0\)

The marginal cost function of manufacturing x gloves is 6 + 10x − 6x². The total  cost of producing a pair of gloves is Rs. 100. Find the total and average cost function.

Solve: \(\frac { dy }{ dx } ={ ae }^{ y }\)

Solve: y(1 - x) - x\(\frac{dy}{dx}\) = 0

Solve: cosx(1 + cos y)dx − sin y(1 + sin x)dy = 0