The order of the differential equation of all circles with centre at (h, k ) and radius ‘a’ is

The solution of the differential equation \(2x\frac{dy}{dx}-y=3\) represents

If p and q are the order and degree of the differential equation \(y=\frac { dy }{ dx } +{ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) +xy=cosx,\) When

The solution of sec²x tan y dx + sec²y tan x dy = 0 is _________

The solution of (x² - ay)dx = (ax - y²)dy is ___________

For each of the following differential equations, determine its order, degree (if exists)
\(\sqrt { \frac { dy }{ dx } } -4\frac { dy }{ dx } -7x=0\)

For each of the following differential equations, determine its order, degree (if exists)
\(y\left( \frac { dy }{ dx } \right) =\frac { x }{ \left( \frac { dy }{ dx } \right) +{ \left( \frac { dy }{ dx } \right) }^{ 3 } } \)

Form the differential equation satisfied by are the straight lines in my-plane.

Solve: \(\frac{dy}{dx}=1+e^{x-y}\)

Solve: \(\frac{dy}{dx}+y=e^{-x}\)

Express each of the following physical statements in the form of differential equation.
A saving amount pays 8% interest per year, compounded continuously. In addition, the income from another investment is credited to the amount continuously at the rate of Rs. 400 per year.

Find the differential equation of the family of all non-vertical lines in a plane.

Find the differential equation of the family of circles passing through the points (a, 0) and (−a, 0).

Form the differential equation for y = e^-2x [A cos 3x-B sin 3x]

Solve: \(\frac{dy}{dx}+y=cos x\)

Solve \(\frac { dy }{ dx } =\frac { x-y+5 }{ 2(x-y)+7 } .\)

Solve:\(\frac { dy }{ dx } \) = (3x+y+4)².

The surface area of a balloon being inflated changes at a constant rate. If initially, its radius 3 units and after 2 seconds it is 5 units, find the radius after t seconds.

Solve: \(\frac { dy }{ dx } \) = (3x+2y+1)²