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Form the differential equation from the following primitive where constants are arbitrary:
y = ax2 + bx + c
Concept: undefined >> undefined
Find the differential equation of the family of curves y = Ae2x + Be−2x, where A and B are arbitrary constants.
Concept: undefined >> undefined
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Find the differential equation of the family of curves, x = A cos nt + B sin nt, where A and B are arbitrary constants.
Concept: undefined >> undefined
Form the differential equation corresponding to y2 = a (b − x2) by eliminating a and b.
Concept: undefined >> undefined
Form the differential equation corresponding to y2 − 2ay + x2 = a2 by eliminating a.
Concept: undefined >> undefined
Form the differential equation corresponding to (x − a)2 + (y − b)2 = r2 by eliminating a and b.
Concept: undefined >> undefined
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(2x + a)2 + y2 = a2
Concept: undefined >> undefined
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(2x − a)2 − y2 = a2
Concept: undefined >> undefined
Form the differential equation of the family of curves represented by the equation (a being the parameter):
(x − a)2 + 2y2 = a2
Concept: undefined >> undefined
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 + y2 = a2
Concept: undefined >> undefined
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 − y2 = a2
Concept: undefined >> undefined
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y2 = 4ax
Concept: undefined >> undefined
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 + (y − b)2 = 1
Concept: undefined >> undefined
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
(x − a)2 − y2 = 1
Concept: undefined >> undefined
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
Concept: undefined >> undefined
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y2 = 4a (x − b)
Concept: undefined >> undefined
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y = ax3
Concept: undefined >> undefined
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 + y2 = ax3
Concept: undefined >> undefined
Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
y = eax
Concept: undefined >> undefined
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
Concept: undefined >> undefined
