Let `u(x)` and `v(x)` satisfy the differential equation `(d u)/(dx)+p(x)u=f(x)` and `(d v)/(dx)+p(x)v=g(x)` are continuous functions. If `u(x_1)` for some `x_1` and `f(x)>g(x)` for all `x > x_1,` prove that any point `(x , y),` where `x > x_1,` does not satisfy the equations `y=u(x)` and `y=v(x)dot`

Let u(x) and v(x) satisfy the differential equation (du)/(dx)+p(x)u=f(x) and (dv)/(dx)+p(x)v=g(x) are continuous functions.If u(x_(1)) for some x_(1) and f(x)>g(x) for all x>x_(1), does not satisfy point (x,y), where x>x_(1), does not satisfy the equations y=u(x) and y=v(x) .

Let u(x) and v(x) be two continous functions satisfying the differential equations (du)(dx) +p(x)u=f(x) and (dv)/(dx)+p(x)v=g(x) , respectively. If u(x_(1)) gt v(x_(1)) for some x_(1) and f(x) gt g(x) for all x gt x_(1) , prove that any point (x,y) ,where x gt x_(1) , does not satisfy the equations y=u(x) and y=v(x) simultaneously.

Let u(x) and v(x) are differentiable function such that (u(x))/(v(x))=7 . If (u'(x))/(v'(x))=p and ((u(x))/(v(x)))^'=q , then (p+q)/(p-q)=

Let f be function satisfying f(x+y)=f(x)+f(y) and f(x)=x^(2)g(x) , for all x and y, where g(x) is a continuous function. Then f'(x) is :

Let u(x) and v(x) are differentiable function such that (u(x))/(v(x))=6 . If (u'(x))/(v'(x))=p and ((u(x))/(v(x)))'=q then value of (p+q)/(p-q) is equal to

Given y=f(u) and u=g(x) Find (dy)/(dx) if y=2u^(3),u=8x-1

Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x))=7.if(u'(x))/(v'(x))=pand((u(x))/(v(x))) '=q," then "(p+q)/(p-q) has the value equal to

Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x))=7.if(u'(x))/(v'(x))=pand((u(x))/(v(x)))'=q," then "(p+q)/(p-q) has the value equal to