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41. The solution of the differential equation, , ” :, ae ws ( 3 pts, x+y? x+y, , , , , , (a) y=xcot (C- x), (b) cos = = (-x +C), , (c) y=xtan(C - x), , 2, (d) X= xtan (C — x), x

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42. Solution of the differential equation, , 43,, , yxy + 2x yP)dx + x(xy - x°y*)dy = 0 is given by, 1, (a) 21og|x|—log| y|-5>=C, , 1, (b) 2log|y|-log|x|-—=c, 81 y|—log| x| >, 1, (c) 2log|x|+log| y|+—=c, sly! sy, 1, d) 21 +1 —=, (d) 2log] y| oglx|+s=C, Solution of the differential equation, x+y-l\dy (x+y+l, xty-2)dx \x+y4+2), when x = 1, y= 1, is, , (x - y) ea, , (@) log =2 (x+y), , , , , , ery, , (0) og ae 2, , , , (x+y)? +2, 2, , , , (c) log, , (d) none of these, , =2(x-y), , The solution of the differential equation, , ee ydx, , =0, is, 2p, , ‘), , x+y zie), , xdx + ydy + ———, x?, , , , (a) y= ale, (b) x= al, C-< -y ‘), , (c) y= =x al 2, (d) none of these

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; 48. Ify dx - x dy+Inxdx=0 , (1) = - 1, then, , "49., , 51., , 52., , (a) yt1+inx= 0 (b) y+1+2Inx=0, (c) 2(y+1)+Inx=0 (d) y+1-ylnx=0, 2, , 1, The differential equation e = +, , , , determines a family of circle with, , (a) variable radii and fixed centre (0, 1), , (b) variable radii and fixed centre (0, -1), , (c) fixed radius 1 and variable centre on x-axis, (d) fixed radius 1 and variable centre on y-axis, , If y dx + ¥° dy = xdy, x ER, y > 0 and y(1) = 1, then, y(- 3) =, , (a) 3 (b) 2 (c) 1 (d) 5, , The solution of y dx + (x + x’y) dy = 0 is, , 1 l, (a) mame = Saale 7, ny (b) ne c, , ], (c) —+Iny =c (d) Iny=cx, , xy, dy, If 7" tan?(x + y), then sin2(x + y) =, , (a) x-y+c (b) 2x-y) +e, (c) xty+e (d) Arty) te

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§3., , 54., , 55., , Si, , If (x + y)? @ — a, y= Owhen x =0, then y= gj, x, , a, (a) 1 (b) tan 1, (c) tanl+1 (d) tanl-1, , If a = sin(x + y) + cos(x + y), y(0) = 0, then, , Co, (a) e-1 (b) —', (c) Xe-1) (d) 1-e€, , , , If (x? - 1) 4 + 2xy = x, y(0) = 0, then y(2) =, , 1, , 1 b) =, (a) (b) ;, , 2, , ~ d) 2, (c) ; (d), , __ dy ; a, If sinx 7+ ycosx = x sinx, then (y - 1) sin x=, (a) c-xsinx (b) c+xcosx, (c) c-xcosx (d) c+xsinx, , Ify =y+ 1, y(0) = 1, then y (In 2) =, (a) 1 (b) 2 (c) 3 (d) 4