`dx/dt+ax=0, x(0)=2`,
`y(0)=1 , dy/dt+by=0`
`3(x(1)=2(y(1)`, and find t if `x(t)=y(t)`

Let x=x(t) and y=y(t) be solutions of the differential equations (dx)/(dt)+ax=0 and (dy)/(dt)+by=0] , respectively, a,b in R .Given that x(0)=2,y(0)=1 and 3y(1)=2x(1) ,the value of "t" ,for which, [x(t)=y(t) ,is :

Let the function x(t) and y(t) satisfy the differential equations (dy)/(dt)+ax=0,(dy)/(dt)+by=0. If x(0)=2,y(0)=1 and (x(1))/(y(1))=(3)/(2), then x(t)=y(t) for t=

If x = f(t) and y = g(t) are differentiable functions of t so that y is a differentiable functions of x and if dx//dt ne 0 then (dy)/(dx) =(dy)/((dt)/((dx)/(dt)) . Hence find dy/dx if x= 2sint and y=cos2t

y=x^(3)-8x+7 and x=f(t). If (dy)/(dx)=2 and x=3 at t=0 then find the value of (dx)/(dt)att=0

If the solution of the equation (d^(2)x)/(dt^(2))+4(dx)/(dt)+3x = 0 given that for t = 0, x = 0 and (dx)/(dt) = 12 is in the form x = Ae^(-3t) + Be^(-t) , then

If a gt0, x=(t+(1)/(t))^(a) and y=a^((t+(1)/(t))) , find (dy)/(dx).

Let f(x) = int_(0)^(x)(t-1)(t-2)^(2) dt , then find a point of minimum.

Find the derivative (dy)/(dx) of the following implicit functions : (a) int_(0)^(y) e^(-t^(2)) dt + int_(0)^(x^(3)) sin ^(2) t dt = 0 (b) int_(0)^(y) e^(t) dt + int _(0)^(x) sin t dt = 0 (c) int _(pi//2)^(x) sqrt(3 - 2 sin^(2)z ) dz + int_(0)^(y) cos t dt = 0

If x=f(t), y=g(t) are differentiable functions of parameter 't' then prove that y is a differentiable function of 'x' and (dy)/(dx)=((dy)/(dt))/((dx)/(dt)),(dx)/(dt) ne 0 Hence find (dy)/(dx) if x=a cos t, y= a sin t.

If y=int_1^(x^3)dt/(1+t^4), find dy/dx.