The degree and order of the differential equation of the family of all parabolas whose axis is x-axis are respectively 1) 2, 1 2) 1, 2 3) 3, 2 4) 2, 3 Solution: (2) 1, 2... View Article
A first-order and first-degree differential equation in variables x and y is characterized by 1) First order of differentiation of y with respect to x and first degree of dy /dx 2) Order of differentiation of y with respect to x and... View Article
The order of the differential equation of the family of all concentric circles centred at (h, k) is 1) 1 2) 2 3) 3 4) 4 Solution: (1) 1 (x - h)2 + (y - k)2 = r2. Order of the differential equation = 1.... View Article
Family y = Ax + A3 of curves represented by the differential equation of degree 1) Three 2) Two 3) One 4) None of these Solution: (1) Three... View Article
The differential equation of all circles in the first quadrant which touches the coordinate axes is of order 1) 1 2) 2 3) 3 4) None of these Solution: (1) 1 The equation of the family of a circle that touch both the axes is (x - a)2 + (y -... View Article
The differential equation of all circles of radius a is of order 1) 2 2) 3 3) 4 4) None of these Solution: (1) 2 The equation of the family of circles of radius a is (x - h)2 + (y - k)2 = a2... View Article
The order of the differential equation whose solution is y = a cos x + b sin x + ce-x is 1) 3 2) 2 3) 1 4) None of these Solution: (1) 3 y = a cos x + b sin x + ce-x is a three-parmeter family of curves, so its... View Article
The order of the differential equation of all circles of radius r, having a centre on the y-axis and passing through the origin is 1) 1 2) 2 3) 3 4) 4 Solution: (1) 1 The equation of a family of circles of radius $r$ passing through the origin and having a... View Article
The order of the differential equation whose solution is x2 + y2 + 2gx + 2fy + c = 0 is 1) 1 2) 2 3) 3 4) 4 Solution: (3) 3 Since this equation has 3 arbitrary constants i. e. g, f, and c therefore order of this... View Article
The order and degree of the differential equation (√dy / dx) – 4 (dy / dx) – 7x = 0 are 1) 1 and 1/2 2) 2 and 1 3) 1 and 1 4) 1 and 2 Solution: (4) 1 and 2... View Article
The order and degree of the differential equation √sinx (dx + dy) = √cosx (dx – dy) is 1) (1, 2) 2) (2, 2) 3) (1, 1) 4) (2, 1) Solution: (3) (1, 1)... View Article
The order of the differential equation of a family of curves represented by an equation containing four arbitrary constants, will be 1) 2 2) 4 3) 6 4) None of these Solution: (2) 4 It is a fundamental concept.... View Article
The relation y = A sin x + B cos x can be represented by the differential equation 1) dy / dx = y 2) d2y / dx2 = y 3) (d2y / dx2) + y = 0 4) None of these Solution: (3) (d2y / dx2) + y = 0... View Article
The solution of (dy / dx) = [y (x log y – y) / [x (y log x – x]) is 1) xy = cyx 2) xy = c 3) (xy)x = c 4) None of these Solution: (1) xy = cyx... View Article
The solution of the differential equation (dy / dx) + (2y / x) = 0 with y (1) = 1 is given by 1) y = 1 / x2 2) y = 1 / y2 3) x = 1 / y 4) x = y Solution: (1) y = 1 / x2... View Article
The differential equation representing the family of curves y2 = 2c (x + √c), where c is a positive number, is of 1) order 1, degree 3 2) order 2, degree 2 3) degree 3, order 3 4) degree 4, order 4 Solution: (1) order 1, degree 3... View Article
A solution of the differential equation (dy / dx)2 – x (dy / dx) + y = 0 is 1) y = 2 2) y = 2x 3) y = 2x - 4 4) y = 2x2 - 4 Solution: (3) y = 2x - 4... View Article
The solution of the differential equation [y (1 + x-1) + sin y] dx + [x + log x + x cos y] dy = 0 is 1) xy + y log x = c 2) xy + x sin y = c 3) xy + y log x + x sin y = c 4) None of these Solution: (3) xy + y log x + x sin y = c... View Article
The solution of the differential equation y dx – x dy + (log x) dx = 0 is 1) y = log x + cx 2) y + 1 + log x = cx 3) y + cx = log (1 / x) 4) None of these Solution: (2) y + 1 + log x = cx... View Article
Solution of x sin (y / x) dy = (y sin (y / x) – x) dx is 1) cos (y / x) = c 2) log (y / x) + log x = c 3) log (y / x) - log x 4) None of these Solution: (4) None of these x sin (y / x)dy... View Article