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

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

y = ae^(3x) + be^(-2x)

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

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

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

Find the differential equation of xy = ae^x + be^(-x) .

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

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 ellipse having foci on x-axis and centre at the origin.

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