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The graph of the function y = f(x) passi...

The graph of the function y = f(x) passing through the point (0, 1) and satisfying the differential equation `(dy)/(dx) + y cos x = cos x` is such that

A

It is constant function

B

It is periodic

C

it is neither an even nor an odd function.

D

it is continuous and differentiable for all x

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`(dy)/(dx)+ycosx=cosx` (linear)
I.F. =`e^(intcosxdx)=e^(sinx)`
Thus, solution is `ye^(sinx)=inte^(sinx)cosxdx=e^(sinx)+c`
When `x=0, y=1`, then c=0
Thus, y=1. Hence, option (1), (2), (4) are true.
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Multiple)
  1. Which one of the following function(s) is/are homogeneous?

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  2. For the differential equation whose solution is (x-h)^2+(y-k)^2=a^2 (a...

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  3. The equation of the curve satisfying the differential equation y((d...

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  4. Which of the following equation(s) is/are linear?

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  5. The solution of (dy)/(dx) = (ax + h)/(by + k) represents a parabola wh...

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  6. The equation of the curve satisfying the differential equation y2(x...

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  7. Identify the statement(s) which is/are true.

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  8. The graph of the function y = f(x) passing through the point (0, 1) an...

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  9. If f(x), g(x) be twice differentiable functions on [0,2] satisfying f'...

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  10. The solution of the differential equation (x^2y^2-1)dy+2xy^3dx=0 is (a...

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  11. y=a e^(-1/x)+b is a solution of (dy)/(dx)=y/(x^2), then (a) ( b ...

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  12. For equation of the curve whose subnormal is constant, then (a) its...

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  13. The solution of (x dx+y dy)/(x dy-y dx)=sqrt((1-x^2-y^2)/(x^2+y^2)) is

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  14. The curve for which the length of the normal is equal to the length...

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  15. In which of the following differential equation degree is not define...

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  16. If y=f(x) is the solution of equation ydx+dy=-e^(x)y^(2)dy, f(0)=1 and...

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  17. A particle falls in a medium whose resistance is propotional to the sq...

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