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Solve the following differential equatio...

Solve the following differential equations
`(dy)/(dx)=sinx*siny`

A

`e^(cosx)tany/2=c`

B

`e^(cosx)tany=c`

C

`cosxtany=c`

D

`cosxsiny=c`

Text Solution

Verified by Experts

The correct Answer is:
A
`dy-sinxsinydx=0`
or `int"cosec "ydy=intsinxdx`
or `logtany/2=-cosx+logc`
or `log(tany/2)/(c )=-cosx`
or `(tany/2)/( c) = e^(-cosx)`
or `e^(cosx)tany/2=c`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Single)
  1. Solve the differential equation (dy)/(dx)=(x(2logx+1))/((siny+ycosy)).

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  2. The solution of the equation (x^2y+x^2)dx+y^2(x-1)dy=0 is given by (a)...

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  3. Solve the following differential equations (dy)/(dx)=sinx*siny

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  4. The solution of (d v)/(dt)+k/m v=-g is (a) ( b ) (c) v=c (d) e^(( e...

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  5. The general solution of the differential equation (dy)/(dx)+sin(x+y)/2...

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  6. if y+x(dy)/(dx)=x(phi(xy))/(phi'(xy)) then phi(xy) is equation to

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

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  8. The solution of the differential equation (x+(x^3)/(3!)+(x^5)/(5!)+)/...

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

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  10. A curve passing through (2,3) and satisfying the differential equat...

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  11. The solution of the differential equation (d^2y)/(dx^2)=sin3x+e^x+x^2 ...

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  12. The solution of the differential equation y^(')y^(''')=3(y^(''))^(2) i...

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  13. The solution of the differential equation y^-8y^=0, where y(0)=1/8,y^(...

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

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

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

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

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  18. The solution of (y+x+5)dy=(y-x+1)dx is (a) ( b ) (c)log(( d ) (e) (f)...

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

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  20. Solutionof the differential equation ydx-xdy+xsqrt(xy)dy=0 is

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