[" 21.Solution of differential equation will be "],[qquad [(dt)/(du)=t(((dg(x))/(du))-t^(2))/(g(x))" is "],[" I."t=(g(x)+C)/(x)]]

The solution of differential equation (dt)/(dx) = (t[d/dx{g(x)}]-t^(2))/(g(x) ) is

(d)/(dx)(int_(f(x))^(g(x))phi(t)dt) is equal to

Number of solution of the equation (d)/(dx)int_(cos x)^( sin x)(dt)/(1-t^(2))=2sqrt(2)in[0,pi] is

(d)/(dx)(int_(f(x))^(g(x)) phi(t)dt) is equal to

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.

(d)/(dx)int_(t^(2))^(x^(3))(dt)/(sqrt(x^(2)+t^(4)))

If y = f(u) is a differentiable functions of u and u = g(x) is a differentiable functions of x such that the composite functions y = f[g(x) ] is a differentiable functions of x then (dy)/(dx) = (dy)/(du) . (du)/(dx) Hence find (dy)/(dx) if y = sin ^(2)x

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 :