Q77Multiple choice
State True or False for the following:
- (i)Integrating factor of the differential of the form dy + p1 x = Q1 is given by e ∫ p1dy .
- (ii)Solution of the differential equation of the type dy + p1 x = Q1 is given by x.I.F. = (I.F) × Q1dy .
- (iii)Correct substitution for the solution of the differential equation of the type = f ( x, y ) , where f (x, y) is a homogeneous function of zero degree is y = vx. DIFFERENTIAL EQUATIONS 203
- (iv)Correct substitution for the solution of the differential equation of the type = g ( x, y ) where g (x, y) is a homogeneous function of the degree zero is x = vy. (v) Number of arbitrary constants in the particular solution of a differential equation of order two is two. (vi) The differential equation representing the family of circles x2 + (y – a)2 = a2 will be of order two. dy y 3 2 2 (vii) The solution of = is y 3 – x 3 = c. dx x (viii) Differential equation representing the family of curves d2y dy y = ex (Acosx + Bsinx) is 2 – 2 + 2y =0 dx dx dy x + 2 y (ix) The solution of the differential equation = is x + y = kx2. dx x xdy y y (x) Solution of = y + x tan is sin = cx dx x x (xi) The differential equation of all non horizontal lines in a plane is d 2x =0 . dy 2