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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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MOTION-DIFFERENTIAL EQUATION -Exercise 4
  1. The angle between the lines whose direction cosines satisfy the equ...

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

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

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

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  5. If (2+sinx) dy/dx + (y+1) cosx =0and y(0) = 1, then y(pi/2) is equal t...

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  6. Let y=g(x) be the solution of the differential equation sin (dy)/(dx...

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  7. Let f(x) be differentiable on the interval (0,oo) such that f(1)=1 and...

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  8. The differential equation (dy)/(dx)=(sqrt(1-y^2))/y determines a fa...

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

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

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  11. If. y (x) satisfies the differential equation y' – y tan x = 2x sec x ...

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

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  13. Let f[0, 1] -> R (the set of all real numbers be a function.Suppose t...

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

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  15. The function y = f(x) is the solution of the differential equation dy/...

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  16. Let y(x) be a solution of the differential eqution (1 +e^x)y' +ye^x = ...

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  17. Consider the family of all circles whose centers lie on the straigh...

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

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  19. If y=y(x) satisfies the differential equation 8sqrt(x)(sqrt(9+sqrt(x))...

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  20. Let f:[0,oo)rarrR be a continuous function such that f(x)=1-2x+overset...

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