If `y(t)` is a solution of `(1+t)dy/dt-t y=1` and `y(0)=-1` then `y(1)` is

If y(t) is a solution of (1+t)(dy)/(dt)-t y=1a n dy(0)=-1 then show that y(1)=-1/2dot

If y(t) is a solution of (1+t)(dy)/(dt)-t y=1a n dy(0)=-1 then show that y(1)=-1/2dot

The solution of (dy)/(dx)-y=1, y(0)=1 is given by

If y(t) satisfies the differential equation y'(t)+2y(t)=2e^(-2t),y(0)=2 then y(1) equals

If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2) ,then (dy)/(dx)=

x=a (t-sin t) , y =a (1-cos t) find dy/dx

let y=t^(10)+1, and x=t^8+1, then (d^2y)/(dx^2) is

If x=(1-t^2)/(1+t^2) and y=(2at)/(1+t^2) , then (dy)/(dx)=

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 x = t + (1)/(t) "and " y = t - (1)/(t) . "then" (dy)/(dx) is equal to