The general solution of the differential equation \(\frac { dy }{ dx } =\frac { y }{ x } \) is

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 slope at any point of a curve y = f (x) is given by \(\frac{dy}{dx}=3x^2\) and it passes through (-1, 1). Then the equation of the curve is

The I.F. of cosec x \(\frac{dy}{dx}+y\) sec² x = 0 is ___________

The differential equation associated with the family of concentric circles having their centres at the origin is _________.

If \(\frac { dy }{ dx } =\frac { x-y }{ x+y } \) then 
1) xdy + y dx = x dx + y dy
2) \(\int { d(xy) } =\int { xdx } +\int { ydy } \)
3) x²-y² + 2xy = c
4) x²-y² - 2xy = c

Solution of \(\frac{dy}{dx}\)+mx = 0 where m<0 is
1) \(\frac{dy}{dx}\) = -m dy
2) y = ce^mx
3) log x = -m y + log x
4) x = ce^-my

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)
\({ x }^{ 2 }\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +{ \left[ 1+{ \left( \frac { dy }{ dx } \right) }^{ 2 } \right] }^{ \frac { 1 }{ 2 } }=0\)

Find value of m so that the function y = e^mx is a solution of the given differential equation.
y '+ 2y = 0

Determine the order and degree (if exists) of the following differential equations: 
dy + (xy − cos x)dx = 0

Solve the following differential equations or show that the solution of 
\(\\ \\ \\ \frac { dy }{ dx } =\sqrt { \frac { 1-{ y }^{ 2 } }{ 1-{ x }^{ 2 } } } \)

Solve: \(\frac{dy}{dx}=1+e^{x-y}\)

Express each of the following physical statements in the form of differential equation.
For a certain substance, the rate of change of vapor pressure P with respect to temperature T is proportional to the vapor pressure and inversely proportional to the square of the temperature.

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

Solve: x\(\frac{dy}{dx}\)+ 2y = x²

Solve the following differential equations:
(ydx-xdy)cot\(\left( \frac { x }{ y } \right) \) = ny² dx

Solve the following differential equations:
tan y\(\frac{dy}{dx}\) = cos(x+y)+cos(x-y)

Solve the Linear differential equation \((1+x+{ xy }^{ 2 })\frac { dy }{ dx } +(y+{ y }^{ 3 })=0\)

A population grows at the rate of 2% per year. How long does it take for the population to double?