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Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^...

Let `y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R ,` where `f^(prime)(x)` denotes `(dy(x))/(dx),` and `g(x)` is a given non-constant differentiable function on `R` with `g(0)=g(2)=0.` Then the value of `y(2)` is______

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Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0)=0,x in R , where f^(prime)(x) denotes (dy(x))/(dx), and g(x) is a given non-constant differentiable function on R with g(0)=g(2)=0. Then the value of y(2) is______

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Let g^(prime)(x)>0a n df^(prime)(x)<0AAx in Rdot Then (f(x+1))>g(f(x-1)) f(g(x-1))>f(g(x+1)) g(f(x+1))

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If f(x) and g(x) are two differentiable functions on R^+ such that xf'(x)+g(x)=0 and xg'(x)+f(x)=0 for all x in R^+and f(1)+g(1)=4, then the value of f"(2).g"(2) is

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ARIHANT MATHS-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

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

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

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

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

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

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  7. If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c...

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

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  9. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

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  10. For the following question, choose the correct answer from the codes (...

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

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

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

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  14. At present a firm is manufacturing 2000 items. It is estimated that th...

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  15. The population p(t) at time t of a certain mouse species satisfies the...

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  16. If (dy)/(dx)=y+3 and y(0)=2, then y(log2) is equal to

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  17. Let I be the purchase value of an equipment and V(t) be the value afte...

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  18. Solution of the differential equation cosxdy=y(sinx-y)dx, 0ltxlt(pi)...

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  19. The differential equation which represents the family of curves y=c(1)...

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  20. The differential equation of the family of circles with fixed radius ...

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