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Integrating factor of the differential e...

Integrating factor of the differential equation `cosx(dy)/(dx)+ysinx=1` is

A

`cosx`

B

`tanx`

C

`secx`

D

`sinx`

Text Solution

Verified by Experts

The correct Answer is:
C
`cosx(dy)/(dx)+ysinx=1`
or `(dy)/(dx)+y(sinx)/(cosx)=secx`
`therefore intPdx=int(sinx)/(cosx)dx`
`=-logcosx`
`=log secx`
`therefore` I.F. `=e^(intPdx)=e^(log secx)=secx`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Single)
  1. The integrating factor of the differential equation (dy)/(dx)(x(log)x)...

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  2. The solution of the differential equation x(x^2+1)((dy)/(dx))=y(1-x^2)...

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  3. Integrating factor of the differential equation cosx(dy)/(dx)+ysinx=1 ...

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  4. Solution of the equation cos^2x(dy/dx)-(tan2x)y=cos^4x, when y(pi/6)=(...

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  5. If integrating factor of x(1-x^2)dy+(2x^2y-y-a x^3)dx=0 is e^(intp dx...

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  6. A function y=f(x) satisfies (x+1)f^(prime)(x)-2(x^2+x)f(x)=(e^x^2)/((x...

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  7. The general solution of the equation (dy)/(dx)=1+x y is (a) ( b ) (...

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  8. The solution of the differential equation (x+2y^3)(dy)/(dx)=y is

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  9. The solution of the differential equation x^2(dy)/(dx)cos(1/x)-ysin(1/...

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  10. The solution of (dy)/(dx)=(x^2+y^2+1)/(2x y) satisfying y(1)=1 is

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  11. The solution of the differential equation (dy)/(dx)=1/(x y[x^2siny^2+1...

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  12. Find the equation of a curve passing through (2,7/2) and having grad...

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  13. Which of the following is not the differential equation of family o...

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  14. Tangent to a curve intercepts the y-axis at a point Pdot A line ...

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  15. Orthogonal trajectories of family of the curve x^(2/3)+y^(2/3)=a^((2/3...

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  16. The curve in the first quadrant for which the normal at any point (...

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  17. The equation of the curve which is such that the portion of the axi...

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  18. The family of curves represented by (dy)/(dx)=(x^(2)+x+1)/(y^(2)+y+1) ...

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  19. A normal at P(x , y) on a curve meets the x-axis at Q and N is the ...

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  20. A curve is such that the mid-point of the portion of the tangent in...

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