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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.

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ARIHANT MATHS-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)
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  2. If f:R-{-1}toR and f is differentiable function satisfies: f((x)+f(y...

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  3. A solution curve of the differential equation (x^2+xy+4x+2y+4)((dy)/(d...

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  4. Let f:(0,oo)rarrR be a differentiable function such that f'(x)=2-(f(...

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  5. Let y(x) be a solution of the differential equation (1+e^(x))y^(')+ye^...

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  6. Let y(x) be a solution of the differential equation (1+e^(x))y'+ye^(x)...

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  7. Solve the differential equation : y sqrt(1-x^2)dy-sqrt(1+y^2)dx=0

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  8. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

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  9. A curve passes through the point (1,(pi)/(6)). Let the slope of the cu...

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  10. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  11. Let f:[0,1]rarrR be a function. Suppose the function f is twice differ...

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  12. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  13. Consider the statements : P : There exists some x IR such that f(x)...

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  14. Differentiate the following w.r.t x (log x)^(cos x)

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  15. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

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  16. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

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  17. Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...

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  18. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

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  19. Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)...

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  20. Let the population of rabbits surviving at a time t be governed by t...

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  21. At present, a firm is manufacturing 2000 items. It is estimated tha...

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