If x = sin t and y = cos pt, then 1) (1 - x2)y2 + xy1 + p2 y = 0 2) (1 - x2)y2 + xy1 - p2 y = 0 3) (1 + x2)y2 - xy1 + p2 y = 0 4) (1 - x2)y2 - xy1 + p2 y = 0 Solution:... View Article
The differential equation of the system of concentric circles with centre (1, 2) is 1) (x - 2) + (y - 1) (dy / dx) = 0 2) (x - 1) + (y - 2) (dy / dx) = 0 3) (x + 1) (dy / dx) + (y - 2) = 0 4) (x + 2) (dy / dx) + (y - 1)... View Article
The order and degree of the differential equation √sin x (dx + dy) = √cos x (dx – dy) are 1) (1, 2) 2) (2, 2) 3) (1, 1) 4) (2, 1) 5) (0, 1) Solution: (3) (1, 1) √sin x (dx + dy) = √cos x (dx - dy) In the above... View Article
The differential equation of all straight lines passing through origin is 1) y = √x (dy / dx) 2) dy / dx = y + x 3) dy / dx = y - x 4) None of these Solution: (4) None of these... View Article
The differential equation whose solution Ax2 + By2 = 1, where A and B are arbitrary constant is of 1) first-order and second degree 2) first order and first degree 3) second-order and first degree 4) second-order and second degree... View Article
The differential equation of all parabolas whose axes are parallel to y-axis, is 1) d3y / dx3 = 0 2) d2x / dy2 = c 3) (d3y / dx3) + (d2x / dy2) = 0 4) (d2x / dy2) + 2 (dy / dx) = c Solution: (1) d3y / dx3 = 0... View Article
The differential equation of the family of straight lines whose slope is equal to y-intercept, is 1) (x + 1) (dy / dx) - y = 0 2) (x + 1) (dy / dx) + y = 0 3) dy / dx = (x - 1) / (y - 1) 4) dy / dx = (x + 1) / (y + 1) Solution: (1)... View Article
The differential equation representing the family of curves y2 = 2c (x + √c), where c > 0 is a parameter is of order and degree as follows, 1) order 2, degree 2 2) order 1, degree 3 3) order 1, degree 1 4) order 1, degree 2 Solution: (2) order 1, degree 3... View Article
The differential equation of the systems of all circles of radius r in the xy-plane is 1) [1 + (dy / dx)3]2 = r2 (d2y / dx2)2 2) [1 + (dy / dx)3]2 = r2 (d2y / dx2)3 3) [1 + (dy / dx)2]3 = r2 (d2y / dx2)2 4) [1 + (dy /... View Article
The differential equation of the family of curves y = e2x (a cos x + b sin x), where a and b are arbitrary constants, is given by 1) y2 - 4y1 + 5y = 0 2) 2y2 - y1 + 5y = 0 3) y2 + 4y1 - 5y = 0 4) y2 - 2y1 + 5y = 0 Solution: (1) y2 - 4y1 + 5y = 0... View Article
The order of the differential equation of all tangent lines to the parabola y = x2 is 1) 1 2) 2 3) 3 4) 4 Solution: (1) 1 The parametric form of the given equation is x = t, y = t2. The equation of any tangent at t... View Article
The family of curves y = ea sin x, where a is an arbitrary constant, is represented by the differential equation 1) log y = tan x (dy / dx) 2) y log y = tan x (dy / dx) 3) y log y = sin x (dy / dx) 4) log y = cos x (dy / dx) 5) y log y = cos x (dy / dx)... View Article
The degree and order of the differential equation y = px + x3 √a2p2 + b2, where p = dy / dx are respectively 1) 3, 1 2) 1, 3 3) 1, 1 4) 3, 3 Solution: (1) 3, 1... View Article
If y = (sin-1 x)2, then (1 – x2) (d2y / dx2) – x (dy / dx) = 1) 0 2) -1 3) -2 4) 1 5) 2 Solution: (5) 2... View Article
The degree of the differential equation satisfying √1 – x2 + √1 – y2 = a (x – y) is 1) 1 2) 3 3) 2 4) None of these Solution: (1) 1... View Article
Order of the equation [1 + 5 (dy / dx)]3/2 = 10 (d3y / dx3) is 1) 2 2) 3 3) 1 4) 0 Solution: (2) 3... View Article
The differential equation of the system of circles touching the y-axis at origin is 1) (dy / dx) = [x2 + y2] / 2xy 2) dy / dx = [y2 - x2] / xy 3) dy / dx = [y2 - x2] / 2xy 4) dy / dx = [x2 - y2] / 2xy Solution: (3) dy / dx =... View Article
The order and degree of differential equation (d3y / dx3)â…˜ – 2 (dy / dx) (d2y / dx2)2 = 0 are 1) 2, 10 2) 3, 10 3) 3, 5 4) 3, 4 Solution: (4) 3, 4... View Article
The differential equation of the family of parabolas with vertex at (0, -1) and having axis along Y – axis is 1) yy' + 2xy + 1 = 0 2) xy' + y + 1 = 0 3) xy' - 2y - 2 = 0 4) xy' - y - 1 = 0 Solution: (3) xy' - 2y - 2 = 0... View Article