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
The integrating factor of the differential equation (y log y)dx = (log y – x) dy is 1) 1/log y 2) log (log y) 3) 1 + log y 4) 1/log (log y) 5) log y Solution: (5) log y... View Article
The equation of one of the curves whose slope at any point is equal to y + 2x is 1) y = 2(ex + x - 1) 2) y = 2(ex - x - 1) 3) y = 2(ex - x + 1) 4) y = 2(ex + x + 1) Solution: (2) y = 2(ex - x - 1)... View Article
The integrating factor of x (dy / dx) + (1 + x) y = x is 1) x 2) 2x 3) ex log x 4) x ex Solution: (4) x ex... View Article
Solution of the differential equations cos x dy = y (sin x – y)dx, 0 < x < Ï€/2, is 1) sec x = (tan x + C) y 2) y sec x = tan x + C 3) y tan x = sec x + C 4) tan x = (sec x + C)y Solution: (1) sec x = (tan x + C) y... View Article
The solution of y dx – x dy + log x dx = 0 is 1) y - log x - 1 = Cx 2) x + log y + 1 = Cx 3) y + logx + 1 = Cx 4) y + log x - 1 = Cx Solution: (3) y + logx + 1 = Cx... View Article
The solution of (x + 2y3) (dy / dx) = y is 1) x = y3 + Cy 2) x = y2 + Cy 3) x3 = y3 + Cy 4) None of these Solution: (1) x = y3 + Cy... View Article
If y (t) is solution of (1 + t) (dy / dt) – ty = 1 and y (0) = – 1, then y (1) = 1) - (1/2) 2) e + 1/2 3) e - 1/2 4) 1/2 Solution: (1) - (1/2)... View Article
Solve (dy / dx) + (y / x) = x3. 1) y = (x4 / 5) + (c / x) 2) y = (x3 / 3) + (c / x) 3) y = (x3 / 3) + (c) 4) y = (x4 / 4) + (c) Solution: (1) y = (x4 / 5) + (c / x)... View Article
The solution of cosy + (x siny – 1) (dy / dx) = 0 1) xsec y = tan y + C 2) tan y - sec y = Cx 3) tan y + sec y = Cx 4) x sec y + tan y = C Solution: (1) xsec y = tan y + C... View Article
Which of the following is a correct solution of x cos x (dy / dx) + y (x sin x + cos x) = 1? 1) y x sec y = C + tan x 2) yx cos y = C + tan x 3) yx secx = C + tan x 4) None of these Solution: (3) yx secx = C + tan x... View Article
The integrating factor of the differential equation (1 + x2) (dy / dx) + y = etan^(-1)x is 1) tan-1 x 2) 1 + x2 3) etan^(-1) x 4) loge (1 + x2) Solution: (3) etan^(-1) x... View Article
If dx + dy = (x + y) (dx – dy), then log (x + y) is equal to 1) x + y + C 2) x + 2y + C 3) x - y + C 4) 2x + y + C Solution: (3) x - y + C... View Article
The solution of the differential equation (x2 – y2) dx + 2xy dy = 0 is 1) x2 + y2 = Cy 2) C(x2 - y2) = x 3) x2 - y2 = Cy 4) x2 + y2 = Cx Solution: (4) x2 + y2 = Cx... View Article
