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The solution of the differential equatio...

The solution of the differential equation `(xcoty + log cosx)dy +(logsiny-ytanx) dx=0` is

A

`(sinx)^(y)(cosy)^(x)=c`

B

`(siny)^(x)(cosx)^(y)=c`

C

`(sinx)^(x)(cosy)^(y)=c`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(xcoty+logcosx)dy+(log siny-ytanx)dx=0`
or `intd(xlogsiny)+intd(ylogcosx)=0`
or `xlogsiny+ylogcosx=logc`
or `(siny)^(x)(cosx)^(y)=c`
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CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
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  3. The solution of the differential equation (xcoty + log cosx)dy +(logsi...

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  4. If dy/dx=(e^y-x)^(-1), where y(0)=0 , then y is expressed explicitly...

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  5. The general solution of the differential equation, y^(prime)+yvarph...

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

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

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  9. Solution of the equation cos^2x(dy)/(dx)-(tan2x)y=cos^4x, where |x|< ...

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  10. 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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  11. 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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  12. The general solution of the equation (dy)/(dx)=1+x y is

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

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

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

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

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  17. The equation of a curve passing through (2,7/2) and having gradient...

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  18. Which of the following is not the differential equation of family of c...

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

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

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