Home
Class 12
MATHS
Let u(x) and v(x) be two continous funct...

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.

Promotional Banner

Similar Questions

Explore conceptually related problems

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

If y=f (x) satisfy the differential equation (dy)/(dx) + y/x =x ^(2),f (1)=1, then value of f (3) equals:

Find the integrating factor of the differential equation: x log x (dy)/(dx)+y=(2)/(x)logx, x gt 1

Let f(x)=x^(3)+x+1 and let g(x) be its inverse function then equation of the tangent to y=g(x) at x = 3 is

The functions u=e^(x).sinx and v=e^(x).cosx satisfy the equation

If y=f(x) satisfies the differential equation (dy)/(dx)+(2x)/(1+x^(2))y=(3x^(2))/(1+x^(2)) where f(1)=1 , then f(2) is equal to

The equation of the curve satisfying the differential equation y(x+y^3)dx=x(y^3-x)dy and passing through the point (1,1) is

If y(x) is the solution of the differential equation ( dy )/( dx) +((2x+1)/(x))y=e^(-2x), x gt 0 , where y(1) = (1)/(2) e^(-2) , then

Let y=f(x) be a solution of the differential equation (dy)/(dx)=(y^(2)-x^(2))/(2xy)(AA x, y gt 0) . If f(1)=2 , then f'(1) is equal to

If P(1)=0a n d(d P(x))/(dx)gtP(x) , for all xge1 . Prove that P(x)>0 for all x>1.