Find the differential equation whose solution represents the family : `c (y + c)^2 = x^3`

Find the differential equation whose solution represents the family y=ae^(3x)+be^(x) .

The differential equation which represents the family of curves y=c_(1)e^(c_(2^(x) where c_(1)andc_(2) are arbitary constants is

Form the differential equation representing the family of curves y = a sin ( x + b) , where a, b are arbitrary constants.

The differential equation corresponding to the family of curves y=e^x (ax+ b) is

Form the differential equation representing the family of ellipse having foci on x-axis and centre at the origin.

Statement I Integral curves denoted by the first order linear differential equation (dy)/(dx)-(1)/(x)y=-x are family of parabolas passing throught the origin. Statement II Every differential equation geomrtrically represents a family of curve having some common property.

Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.

Statement 1 : The order of the differential equation whose general solution is y==c_1cos2x+c_2sin^2x+c_3cos^2x+c_4e^(2x)+c_5e^(2x+c_6) is 3. Statement 2 : Total number of arbitrary parameters in the given general solution in the statement (1) is 3.

In each of the Exercises 1 to 5, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. 1. (x)/(a) + (y)/(b) = 1

Find the separate equation of lines represented by the equation by the equation x^2-6xy+8y^2=0