The general solution of the differential equation d2y / dx2 + 8 (dy / dx) + 16y = 0 is 1) (A + Bx) e5x 2) (A + Bx) e-4x 3) (A + Bx2) e4x 4) (A + Bx4) e4x Solution: (2) (A + Bx) e-4x... View Article
For the population p (t) at time t of a certain mouse species, the differential equation dp (t) / dt = 0.5 (t) – 450. If p (0) = 850, then the time at which the population becomes zero is 1) 2 log 18 2) log 9 3) 1/2 log 18 4) log 18 Solution: (1) 2 log 18... View Article
A present, a firm is manufacturing 1000 items, It is estimated that the rate of change of production P with respect to the additional number of workers x is given by dp/dx = 100 – 12√x. If the firm employs 25 more workers, then the new level of production of the item is 1) 2500 2) 3000 3) 3500 4) 4500 Solution: (3) 3500... View Article
A gardener is digging a plot of land. As he gets tried, he works more slowly. After t min, he is digging at a rate of 2/√t m2/min. How long will take him to dig an area of 40 sqm? 1) 100 min 2) 10 min 3) 30 mm 4) 40 min Solution: (1) 100 min... View Article
The equation of the curve for which the square of the ordinate is twice the rectangle contained by the abscissa and the intercept of the normal on X – axis and passing through (2,1) is 1) x2 + y2 - x = 0 2) 4x2 + 2y2 - 9y = 0 3) 2x2 + 4y2 - 9x = 0 4) 4x2 + 2y2 - 9x = 0 Solution: (4) 4x2 + 2y2 - 9x = 0... View Article
The solution of dy = cos x (2 – y cosec x) dx, where y = 2, where x = Ï€ / 2 is 1) y = sin x + cosec x 2) y = tan (x / 2) + cot (x / 2) 3) y = (1 / √2) sec (x / √2) + √2 cos (x / 2) 4) None of the above Solution:... View Article
The solution of the differential equation x (dy / dx) + y = x cos x + sin x, given that y = 1 when x = π / 2 is 1) y = sin x - cos x 2) y = cos x 3) y = sin x 4) y = sin x + cos x Solution: (3) y = sin x... View Article
The solution of the differential equation (dy / dx) + (y / x) = sin x is 1) x (y + cos x) = sin x + c 2) x (y - cos x) = sin x + c 3) x (y cos x) = sin x + c 4) x (y - cos x) = cos x + c 5) x (y + cos x) =... View Article
An integrating factor of the differential equation (1 + y + x2 y) dx + (x + x3)dy = 0 is 1) log x 2) x 3) ex 4) 1/x 5) - (1/x) Solution: (2) x... View Article
The solution of the differential equation x (dy / dx) + 2y = x2 is 1) y = [x2 + c] / 4x2 2) y = (x2 / 4) + c 3) y = [x4 + c] / x2 4) y = [x4 + c] / 4x2 Solution: (4) y = [x4 + c] / 4x2... View Article
To reduce the differential equation (dy / dx) + P (x) . y = Q (x) . yn to the linear form, the substitution is 1) v = 1 / yn 2) v = 1 / yn-1 3) v = yn 4) v = yn-1 Solution: (2) v = 1 / yn-1 The equation is of the form (dy / dx) + Py = Qyn.... View Article
The solution of the differential equation (dy / dx) + (tan y / x) = [tan y sin y] / x2 is 1) 2x = sin y (1 + cx2) 2) (y / sin x) + log x = c 3) log x + x = c 4) log x + y = c Solution: (1) 2x = sin y (1 + cx2)... View Article
The solution of (x + y + 1) (dy / dx) = 1 is 1) y = (x + 2) + cex 2) y = - (x + 2) + cex 3) x = - (y + 2) + cey 4) x = (y + 2)2 + cey Solution: (3) x = - (y + 2) + cey... View Article
The solution of the differential equation dy / dx = y tan x – 2 sin x, is 1) y sin x = c + sin 2x 2) y cos x = c + (1 / 2) sin 2x 3) y cos x = c - sin 2x 4) y cos x = c + (1 / 2) cos 2x Solution: (4) y cos x... View Article
If the integrating factor of the differential equation (dy / dx) + p (x) y = Q (x) is x, then P (x) is 1) x 2) x2/2 3) 1/x 4) 1/x2 5) 1/2x Solution: (3) 1/x... View Article
The solution of the differential equation (dy / dx) + (2x / (1 + x2)) . y = 1 / (1 + x2)2 is 1) y (1 - x2) = tan-1 x + c 2) y (1 + x2) = tan-1 x + c 3) y (1 + x2)2 = tan-1 x + c 4) y (1 - x2)2 = tan-1 x + c Solution: (2) y (1... View Article
The solution (1 + x2) (dy / dx) + 2xy – 4x2 = 0 is 1) 3x (1 + y2) = 4y3 + c 2) 3y (1 + x2) = 4x3 + c 3) 3x (1 - y2) = 4y3 + c 4) 3y (1 + y2) = 4x3 + c Solution: (2) 3y (1 + x2) = 4x3 +... View Article
The solution of the differential equation (dy / dx) – y tan x = ex sec x is 1) y = ex cos x + c 2) y cos x = ex + c 3) y = ex sin x + c 4) y sin x = ex + c Solution: (2) y cos x = ex + c... View Article
The solution of the differential equation (dy / dx) = [x + y] / x satisfying the condition y (1) = 1 is 1) y = x log x + x 2) y = log x + x 3) y = x log x + x2 4) y = xe(x - 1) Solution: (1) y = x log x + x... View Article
The integrating factor of the differential equation x log x (dy / dx) + y = 2 log x is given by 1) ex 2) log x 3) log (logx) 4) x Solution: (2) log x... View Article