" 3."y=mx+(a)/(m);m" is the arbitrary constant and "a" is a parameter."

c(y+c)^2=x^3 , c is an arbitrary constant.

Form of the differential equation of all family of lines y=mx+(4)/(m) by eliminating the arbitrary constant m is

On finding the differential equation corresponding to y=e^(mx) where m is the arbitrary constant, then m is _________.

y=ae^(2x)+be^(-3x) , a and b being arbitrary constants.

If the least value of the area bounded by the line y=mx+1 and the parabola y=x^(2)+2x-3 is alpha where m is a parameter then the value of (6 alpha)/(32)

Prove by using definition of indefinite integral : int " cosec" mx cot mx dx = - ("cosec "mx)/m + c where m != 0 is a constant independent of x and c is an arbitrary constant .

Prove by using definition of indefinite integral : int sec^(2) mx dx = (tan mx )/m + c where m != 0 is a constant independent of x and c is an arbitrary constant .

Prove by using definition of indefinite integral : int cos mx dx = (sin mx )/m +c where m != 0 is a constant independent of x and c is an arbitrary constant .

In each of the following cases, from the differential equation by eliminating the arbitrary constants from the given equation: y=Ae^(-mx)+Be^(-mx) , A and B are arbitrary constants.