The solution of dy / dx = [ax + h] / [by + k] represents a circle, when 1) a = b 2) a = - b ≠0 3) a = - 2b = 0 4) a = 2b Solution: (2) a = - b ≠0 dy / dx = [ax + h] / [by + k] (ax + h) dx = (by + k)... View Article
Solution of the differential equation xdy – ydx = 0 represents a 1) parabola 2) circle 3) hyperbola 4) straight line Solution: (4) straight line... View Article
The solution of edy/dx = x, when x = 1 and y = 0 is 1) y = x (log x - 1) + 4 2) y = x (log x - 1)+3 3) y = x (log x + 1) + 1 4) y = x (log x - 1) + 1 Solution: (4) y = x (log x - 1) + 1... View Article
A solution of the differential equation (dy / dx)2 – x (dy / dx) + y = 0 1) y = 2x 2) y = - 2x 3) y = 2x - 4 4) y = 2x + 4 Solution: (3) y = 2x - 4... View Article
Which one of the following is the correct solution of (dy / dx) tan y = sin (x + y) + sin (x – y)? 1) sec x = C - 2 sec y 2) sec y = C + 2 cos y 3) sec y = C - 2 cos x 4) sec x = C - 2 cos y Solution: (3) sec y = C - 2 cos x... View Article
The differential equation of the family of curves y = a cos (x + b) is 1) (d2y / dx2) - y = 0 2) (d2y / dx2) + y = 0 3) (d2y / dx2) + 2y = 0 4) None of these Solution: (2) (d2y / dx2) + y = 0... View Article
If y = a sin (5x + c), then 1) dy / dx = 5y 2) dy / dx = - 5y 3) d2y / dx2 = - 25y 4) d2y / dx2 = 25y Solution: (3) d2y / dx2 = - 25y y = a sin (5x + c) dy /... View Article
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