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The solution of the differential of the ...

The solution of the differential of the differential equation
` (dy)/(dx) = sin (x+y) tan (x+y) -1 ` is

A

`"cosec" (x+y) +tan (x+y) = x +C`

B

`x + "cosec" (x+y) = C`

C

` x+ tan (x+y)=C`

D

`x+sec (x+y)=C`

Text Solution

Verified by Experts

The correct Answer is:
b
Given , ` (dy)/(dx) = sin (x+y) tan (x+y) -1`
Put ` x + y = x rArr 1 + (dy)/(dx) = (dz)/(dx)`
` :. (dz)/(dx) -1 sin z tan z - 1` On integrating ,we get
` :. int 1/(t^(2)) dt = x - C rArr -1/t = x - C`
`rArr - "cosec " z = x - C`
` rArr x + "cosec " (x+y) = C " " [ :' z = x + y ]`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIAL EQUATION-PRACTICE EXERCISE (Exercise 2 )
  1. The solution of the differential equation (dy)/(dx)=(a x+g)/(b y+f) re...

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  2. The solution of the differential equation (dy)/(dx)=(a x+g)/(b y+f) re...

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  3. The solution of the differential of the differential equation (dy)/...

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

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  5. The solution of differential equation cos x dy = y (sin x - y ) dx,...

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  6. The equation of one of the curves whose slope of tangent at any point ...

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  7. The general solution of the differential equation (dy)/(dx)+(1+cos2y)/...

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

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  9. The solution of differential equation [ e^(-2sqrt(2))/(sqrt(x))-y/(...

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  10. The integrating factor of the differential equation (y log y) dx = (l...

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

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  12. Integrating factor of the differential equation (x.logx)(dy)/(dx)+y=2l...

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  13. Solution of the equation x^(2)y - x^(3)(dy)/(dx)=y^(4)cosx , when y(0)...

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

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  15. The solution of the differential equation (dy)/(dx)=(x+y)/x satisfyi...

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  16. The integrating factor of the differential equation (dy)/(dx)+(y)/((1-...

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  17. The solution of the differential equation (dy)/(dx)-y tan x=e^(x)sec x...

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  18. (1 + x^(2)) (dy)/(dx) + 2xy = 4x ^(2), given that y = 0, when x =0

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

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

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