The differential equation \({ \left( \frac { dx }{ dy } \right) }^{ 3 }+2{ y }^{ \frac { 1 }{ 2 } }\) = x is ______.

The integrating factor of the differential equation \(\frac{dx}{dy}+Px=Q\) is ______.

The complementary function of (D²+ 4)y = e^2x is ______.

The particular integral of the differential equation is \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -8\frac { dy }{ dx } \) + 16y = 2e^4x ______.

Solution of \(\frac { dy }{ dx } \) + Px = 0 ______.

The differential equation satisfied by all the straight lines in xy plane is _____________

If y = k.e^λx then its differential equation where k is arbitrary constant is _____________

The differential equation obtained by eliminating a and b from y = a e^3x + b e^-3x is _____________

The differential equation formed by eliminating A and B from y = e^x (A cos x + B sin x) is _____________

The degree of the differential equation \(\sqrt { 1+\left( \frac { { d }y }{ dx } \right) ^{ \frac { 1 }{ 3 } } } =\frac { { d }^{ 2 }y }{ dx^{ 2 } } \) is _____________

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.

Solve: ydx − xdy = 0

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

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

Solve the differential equation \(\frac { dy }{ dx } =\frac { x-y }{ x+y } \)

Solve: (3D² + D - 14)y = 4 - 13\({ e }^{\frac{-7}{3}x}\)

Suppose that the quantity demanded \({ Q }_{ d }=29-2p-5\frac { dp }{ dt } +\frac { { d }^{ 2 }p }{ { dt }^{ 2 } } \) and quantity supplied Q_s = 5 + 4p where p is the price. Find the equilibrium price for market clearance.

Find the differential equation of all circles x² +y² + 2gx = 0 which pass through the origin and whose centres are on the X-axis.

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.

The net profit p and quantity x satisfy the differential equation \(\frac { dp }{ dx } =\frac { 2{ p }^{ 3 }-{ x }^{ 3 } }{ 3x{ p }^{ 2 } } \). Find the relationship between the net profit and demand given that p = 20, when x = 10.