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The differential equation which represen...

The differential equation which represents the family of curves `y=c_(1)e^(c_(2^(x)` where `c_(1)andc_(2)` are arbitary constants is

A

`y' = y^2`

B

`y'' = y'y`

C

`yy'' =y'`

D

`yy'' = (y')^2`

Text Solution

Verified by Experts

The correct Answer is:
D
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MOTION-DIFFERENTIAL EQUATION -Exercise 4
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  2. The solution of the differential equation (dy)/(dx)=(x+y)/x satisfy...

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

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  4. The solution of differential equation cos x dy = y (sin x - y ) dx,...

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

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

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

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

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  9. The angle between the lines whose direction cosines satisfy the equ...

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

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

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

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

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

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

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

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

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

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

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