The differential equation which represents the family of curves `y=e^(C x)` is `y_1=C^2y` b. `x y_1-I n\ y=0` c. `x\ I n\ y=y y_1` d. `y\ I n\ y=x y_1`

The differential equation which represents the family of curves y""=""c_1e^(c_2x) , where c_1"and"c_2 are arbitrary constants, is (1) y '=""y^2 (2) y ' '=""y ' y (3) y y ' '=""y ' (4) y y ' '=""(y ')^2

Solve the differential equation x^2dy+y(x+y)dx=0, given that y=1\ w h e n\ x=1.

Solve the differential equation x^2dy+y(x+y)dx=0, given that y=1\ w h e n\ x=1.

STATEMENT-1 : y = e^(x) is a particular solution of (dy)/(dx) = y . STATEMENT-2 : The differential equation representing family of curve y = a cos omega t + b sin omega t , where a and b are parameters, is (d^(2)y)/(dt^(2)) - omega^(2) y = 0 . STATEMENT-3 : y = (1)/(2)x^(3)+c_(1)x+c_(2) is a general solution of (d^(2)y)/(dx^(2)) = 3x .

A differential equation associated to the primitive y=a+b e^(5x)+c e^(-7x) is (where y_n is n t h derivative w.r.t. x) (a) y_3+2y_2-y_1=0( b )4y_3+5y_2-20y_1=0 (c)y_3+2y_2-35y_1=0 (d) none of these

The solution of the differential equation (dy)/(dx)-(y(x+1))/x=0 is given by a. y=x e^(x+C) b. x=y e^x c. y=x+C d. x y=e^x+C

If \ ^n C_x=\ \ ^n C_y\ a n d\ x!=y ,\ t h e n\ x+y=ndot

The general solution of the differential equation (y dx-x dy)/y=0 is(A) x y = C (B) x=C y^2 (C) y = C x (D) y=C x^2

The following line(s) is (are) tangent to the curve y=x^2 - x (A) x-y=0 (B) x+y=0 (C) x-y=1 (D) x+y=1

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1