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

Solve: (1 − x)dy − (1 + y)dx = 0

Solve: \(\frac { dy }{ dx } \) = y sin 2x

Find the curve whose gradient at any point P(x, y) on it is \(\frac { x-a }{ y-b } \) and which passes through the origin.

Solve \(\frac { dy }{ dx } +\frac { y }{ x } ={ x }^{ 3 }\)

Solve the following:
\(\frac { dy }{ dx } -\frac { y }{ x } =x\)

Solve the following:
\(\frac { dy }{ dx } +ycosx=sinx\ cosx\).

Solve \(\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } -\frac { 3dx }{ dt } +2x\) = 0 given that when t = 0, x = 0 and \(\frac { dx }{ dt } \) = 1

(D²−2D−15)y = 0 given that \(\frac{dy}{dx}\)= 0 and \(\frac{d^2 y}{dx^2}\) = 2 when x = 0

Solve the following differential equations: (4D²+4D−3)y = e^2x

Solve : (D²−4D−1)y = e^−3x

Form the differential equation having for its general solution y = ax² + bx

Solve yx²dx + e ^{− x}dy = 0

Solve x \(\frac{dy}{dx}\) + 2y = x⁴

Solve \(\frac { dy }{ dx } =xy+x+y+1\)

Find the differential equation of the following
y = c (x − c)²

Solve: \(\frac { 1+{ x }^{ 2 } }{ 1+y } =xy\frac { dy }{ dx } \)

Solve: log\(\left( \frac { dy }{ dx } \right) \) = ax + by