The integrating factor of x\(\frac { dy }{ dx } \)-y = e^x is _____________

In (x²-y²)dy = 2xy dx, if we put y = vx, then the equation is transformed into _____________

The solution of \(\frac { dp }{ dt } \) = ke^-t (k is a constant) is _____________

The solution of \(\frac { dy }{ dx } \) = e^x-y is _____________

The solution of xdx +ydy = 0 is

The degree and order of \(\frac { { d }^{ 2 }y }{ dx^{ 2 } } -6\sqrt { \frac { dy }{ dx } } \)= 0 are _____________

The degree of c =\(\frac { \left[ 1+\left( \frac { dy }{ dx } \right) ^{ 3 } \right] ^{ 2/3 } }{ \frac { d^{ 3 }y }{ dx^{ 3 } } } \) where c is a constant 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 _____________

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

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

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

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

The amount present in a radio active element disintegrates at a rate proportional to its amount. The differential equation corresponding to the above statement is _____________ (k is negative).

The differential equation of all circles with centre at the origin is _____________

The differential equation \(\left( \frac { dx }{ dy } \right) ^{ 2 }+5y^{ \frac { 1 }{ 3 } }\)= x is _____________