5 point 0 2 and satisfying the differential equation through the dy dx 7 y cos x cos x is such that 1 It is a differentiable function VXER 2 It is continuous VXE R 3 It is periodic 4 It is passing through 1 2 Orthogonal 2 dy dx trajectories of the system of curves a are X 1 9a y c 2 4x 3 y c x3 2 3 a 4 9a y c 4x 6 A curve has the property that area of triangle formed by the x axis the tangent to the curve and radius vector of the point of tangency is k The equation of all such curves passing through 0 1 is X a k 2y by then 2 X312 9 a 2 y c 0 8 odE 2 b 1 Juice 4 b 2 1 a 1 3 a 2 The tangent at any point P of a curve C meets the x axis at Q whose abscissa is positive and OP OQ O being the origin the equation of curve C satisfying these conditions may be 1 y 1 4x 2 y 9 12x 3 16 16x 4 y 25 20x Consider a curved mirror y f x passing through 8 6 having the property that all light rays emerging from origin after getting reflected from the mirror becomes parallel to x axis The equation of the mirror is ya blc 9 The equation of all possibl orthogonal to the family of c x y 2 2cx 0 where c is 2 1 x y ky 0 3 x y kx 0 4 10 If a mothball loses volume b proportional to its instantane of the ball decreases from 2 so the time before which the is less than or equal to 1 4 months 3 2 months 11 Let x 1 x dy dx x y 1 General solution of g xy 1 x In 1 x 2 General solution of c xy 1 x In 1 x Instner to eqois or arti 3 It y f x is a sol equation then lim X 4 If y f x is solution then lim f x 1 X 1 12 Let a curve passes th differential equation 1 It represents equ 2 It represents equ 3 Area enclosed b 4 Line y 1 is a ta 13 A curve satisfie dy x 1 xy dx x y y 1 The equation c x y 2x 2 an