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Solve x((dy)/(dx))=y(logy-logx+1)...

Solve `x((dy)/(dx))=y(logy-logx+1)`

A

`logx/y=cy`

B

`logy/x=cy`

C

`logy/x=cx`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(dy)/(dx)= y/x[logy/x+1]`
Put `y=vx`
`v+x(dv)/(dx) = vlogv+v`
`therefore (dv)/(vlogv) = (dx)/x`
`therefore log(logv)=logx+logc=logcx`
`therefore logy/x=cx`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Single)
  1. The solution of the differential equation y^(prime prime prime)-8y^(pr...

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  2. The slope of the tangent at (x , y) to a curve passing through (1,p...

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  3. Solve x((dy)/(dx))=y(logy-logx+1)

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  4. The solution of differential equation x y^(prime)=x((y^2)/(x^2)+(f((y^...

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  5. The solution of (x^2+x y)dy=(x^2+y^2)dx is (a) ( b ) (c)logx=log(( d ...

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  6. The solution of (y+x+5)dy=(y-x+1)dx is

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  7. The slope of the tangent at (x , y) to a curve passing through a po...

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  8. Solution of the differential equation ydx-xdy+xsqrt(xy)dy=0 is

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  9. The solution of (x^2dy)/(dx)-x y=1+cosy/x is (a) ( b ) (c)tan(( d ) (...

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

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  11. Solution of the differential equation {1/x-(y^2)/((x-y)^2)}dx+{(x^2)/(...

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  12. The solution of differential equation (2y+x y^3)dx+(x+x^2y^2)dy=0 is (...

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  13. Find the solution of y e^(-x/y)dx-(x e^((-x/y))+y^3)dy=0 is

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  14. Find the curve satisfying the equation (dy)/(dx)=(y(x+y^3))/(x(y^3-x))...

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  15. Find the solution of differential equation (x+y(dy)/(dx))/(y-x(dy)/(...

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  16. The solution of the differential equation (dy)/(dx)=(3x^2y^4+2x y)/(x^...

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  17. The solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt...

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  18. The solution of differential equation (y(2x^4+y)dy)/(dx)=(1-4x y^2)x^2...

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  19. The solution of the differential equation (xcoty+logcosx)dy+(logsiny-y...

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  20. If =(e^y-x)^(-1), where y(0)=0 , then y is expressed explicitly as ...

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