The differential equation obtained on eliminating A and B from `y=A cos\ omegat+bsinomegat ,` is (a)`y^(primeprime)+ y^(prime)=0` (b.) `y^(primeprime)+omega^2y=0` (c.) `y^(primeprime)=omega^2y` (d.) `y^(primeprime)+y=0`

The solution of the differential equation y^(prime)y^(primeprimeprime)=3(y^(primeprime))^2 is

The solution of the differential equation y^(primeprimeprime)-8y^(primeprime)=0, where y(0)=1/8,y^(prime)(0)=0,y''(0)=1 , is

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.

If x^2+y^2=1,t h e n (a) y y^('')-2(y^(prime))^2+1=0 (b) yy^('')+(y^(prime))^2+1=0 (c) y y^('')+(y^(prime))^(-2)-1=0 (d) y y^('')+2(y^(prime))^2+1=0

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 .

If y(x) satisfies the differential equation y'-y tan x=2x and y(0)=0 , then

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a) f^(primeprime)(x)=f(x)=0 (b) 4f^(primeprime)(x)+f(x)=0 (c) f^(primeprime)(x)+f(x)=0 (d) 4f^(primeprime)(x)-f(x)=0

The differential equation of the family of curves y=A(x+B)^2 after eliminating A and B is (A) yy\'\'=y\'^2 (B) 2yy\'\'=y\'-y (C) 2yy\'\'=y\'+y (D) 2yy\'\'=y\'^2

If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c x and y(0)=0 , then