The solution of the differential equation (3xy + y2)dx + (x2 + xy)dy = 0 is 1) x2 (2xy + y2) = C2 2) x2 (2xy - y2) = C2 3) x2(y2 - 2xy2) = C2 4) None of these Solution: (1) x2 (2xy + y2) = C2... View Article
The general solution of the differential equation dy / dx = [x + y + 1] / [2x + 2y + 1] is 1) loge |3x + 3y + 2|+ 3x + 6y = C 2) loge |3x + 3y + 2|- 3x + 6y = C 3) loge |3x + 3y + 2|- 3x - 6y = C 4) loge |3x + 3y + 2|+ 3x - 6y... View Article
The solution of the differential equation (x2 + y2) dx – 2xy dy = 0 is 1) x2 - y2 = Cx 2) x2 - y2 = Cy 3) x2 + y2 = Cx 4) x2 + y2 = Cy Solution: (1) x2 - y2 = Cx... View Article
If C is an arbitrary constant, then the general solution of the differential equation y dx – xdy = xydx is given by 1) y = Cxe-x 2) y = Cye-x 3) y + ex = Cx 4) yex = Cx Solution: (1) y = Cxe-x... View Article
The solution of dy / dx = 3x+y is 1) 3x+y = c 2) 3x + 3y = c 3) 3x-y = c 4) 3x + 3-y = c Solution: (4) 3x + 3-y = c... View Article
The solution of [dy / dx] + 1 = ex+y is 1) e-(x+y) + x + c = 0 2) e-(x+y) - x + c = 0 3) ex+y + x + c = 0 4) ex+y - x + c = 0 Solution: (1) e-(x+y) + x + c = 0... View Article
The general solution of the differential equation (1 + y2)dx + (1 + x2) dy = 0 is 1) x - y = C (1 - xy) 2) x - y = C (1 + xy) 3) x + y = C (1 - xy) 4) x + y = C (1 + xy) Solution: (3) x + y = C (1 - xy)... View Article
The differential equation dy / dx = [x (1 + y2)] / [y (1 + x2)] represents a family of 1) parabola 2) hyperbola 3) circle 4) ellipse Solution: (2) hyperbola... View Article
The equation of curve through point (1, 0) which satisfies the differential equation (1 + y2) dx – xy dy = 0, is 1) x2 + y2 = 4 2) x2 - y2 = 1 3) 2x2 + y2 = 2 4) None of these Solution: (2) x2 - y2 = 1... View Article
The solution of the differential equation (dy / dx) = (4x + y + 1)2 is 1) (4x + y + 1) = tan (2x + C) 2) (4x + y + 1)2 = 2 tan (2x + C) 3) (4x + y + 1)3 = 3 tan (2x + C) 4) (4x + y + 1) = 2 tan (2x + C)... View Article
The solution of the differential equation (dy / dx) = [x – 2y + 1] / [2x – 4y] is 1) (x - 2y)2 + 2x = C 2) (x - 2y)2 + x = C 3) (x - 2y) + 2x2 = C 4) (x - 2y) + x2 = C Solution: (1) (x - 2y)2 + 2x = C... View Article
The solution of the differential equation 9y (dy/dx) + 4x = 0 is 1) (y2 / 9) + (x2 / 4) = c 2) (y2 / 4) + (x2 / 9) = c 3) (y2 / 9) - (x2 / 4) = c 4) (y2) - (x2 / 9) = c Solution: (2) (y2 / 4) + (x2... View Article
The solution of the differential equation (x + y)2 (dy / dx) = a2 is 1) (x + y)2 (dy / dx) = (a2x / 2) + c 2) (x + y)2 (dy / dx) = (a2x) + c 3) (x + y)2 (dy / dx) = (2a2x) + c 4) None of these Solution:... View Article
The differential equation y (dy/dx) + x = c represents 1) a family of hyperbolas 2) a family of circles whose centres are on the y-axis 3) a family of parabolas 4) a family of circles whose... View Article
The solution of the differential equation dy / dx = [x – y + 3] / [2 (x – y) + 5] is 1) 2(x - y) + log (x - y) = x + C 2) 2(x - y) - log (x - y + 2) = x + C 3) 2(x - y) + log (x - y + 2) = x + C 4) None of the above... View Article
The solution of the equation y – x (dy / dx) = a [y2 + (dy / dx)] is 1) y = C (x + a)(1 - ay) 2) y = C (x + a)(1 + ay) 3) y = C(x - a)(1 + ay) 4) None of these Solution: (1) y = C (x + a)(1 - ay)... View Article
The solution of the differential equation dy / dx = [xy + y] / [xy + x] is 1) x + y = log (cy / x) 2) x + y = log (cxy) 3) x - y = log (cx / y) 4) y - x = log (cx / y) Solution: (4) y - x = log (cx / y)... View Article
The solution of the differential equation dy / dx = sin (x + y) tan (x + y) – 1 is 1) cosec (x + y) + tan (x + y) = x + C 2) x + cosec (x + y) = C 3) x + tan (x + y) = C 4) x + sec (x + y) = C Solution: (2) x + cosec... View Article
The solution of differential equation (1 + x)y dx + (1 – y)x dy = 0 is 1) loge (xy) + x - y = C 2) loge (x / y) + x + y = c 3) loge (x / y) - x + y = c 4) loge (xy) - x + y = C Solution: (1) loge (xy) + x... View Article
General solution of the differential equation dy / dx = [x + y + 1] / [x + y – 1] is given by 1) x + y = log |x + y| + c 2) x - y = log |x + y| + c 3) y = x + log |x + y| + c 4) y = x log |x + y| + c Solution: (3) y = x + log... View Article
