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
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