Find the Differential equation satisfying
the family of curves `y^2=a(b^2-x^2)`,a and b
are arbitrary constants.

Find the Differential equation satisfying the family of curves y=ae^(3x)+be^(-2x) ,a and b are arbitrary constants.

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

The differential equation representing the family of curves y^(2) = a(ax + b) , where a and b are arbitrary constants, is of

Form the differential equation representing the family of curve given by (x-a)^2+2y^2=a^2 ,a is a arbitrary constants.

The differential equation representing the family of curves given by y=ae^(-3x)+b , where a and b are arbitrary constants, is a) (d^(2)y)/(dx^(2))+3(dy)/(dx)-2y=0 b) (d^(2)y)/(dx^(2))-3(dy)/(dx)=0 c) (d^(2)y)/(dx^(2))-3(dy)/(dx)-2y=0 d) (d^(2)y)/(dx^(2))+3(dy)/(dx)=0

The differential equation of the family of curves y= e^(x) (A cos x + B sin x) , where A and B are arbitrary constants is a) y''-2y'+2y=0 b) y''+2y'-2y=0 c) y''+y^(2)+y=0 d) y''+2y'-y=0