61.Form the differential equation representing the family of curves y = a cos (x + b) where a and b are arbitrary constants.
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62.Find the differential equation of the family of curves  y = A sin mx + B cos mx. where m is fixed, and A and B are arbitrary constants.
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63.Form the differential equation corresponding to y2 = m (a2 – x2) by eliminating m and a.
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64.Form the differential equation corresponding to y2 = a (b – x) (b + x) by eliminating a and b.
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65.Form the differential equation of the family of curves represented by the equation (x – a)2 + 2 y2 = a2, a being the parameter.
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Long Answer Type
66.Prove that x2 – y2 = c (x2 + y2 )2 is the general solution of differential equation (x3 – 3 x y2 ) dx = (y3 –3 x2 y) dy . where c is a parameter.
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Short Answer Type
67.Form a differential equation from the equation y = 2(x2Â - 1) + ce-x2.
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68.Form the differential equation of the family of curves where A and B are constants.
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69.Form the differential equation of the family of curves where A and B are constants.
70.Form the differential equation of the family of curves where A and B are constants.
The given equation is                            ...(1)                             which is required differential equation.Â
Short Answer Type
Long Answer Type
             ...(1)
                            
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