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The solution of x (dy)/(dx) = y+2 sqrt(...

The solution of ` x (dy)/(dx) = y+2 sqrt(y^(2)-x^(2))` is

A

` 1/2 In ((y+sqrt(y^(2)-x^(2)))/x)= In Cx`

B

` 1/2 In ((y-sqrt(y^(2)-x^(2)))/x)= In Cx`

C

` 1/2 In (y - sqrt(y^(2)-x^(2)))= In Cx `

D

` In (y - sqrt(y^(2) - x^(2))) = In Cx`

Text Solution

Verified by Experts

The correct Answer is:
a
Putting ` y = vx and (dy)/(dx) = v +x(dy)/(dx),`
we get ` xv + x^(2) (dv)/(dx) = vx + 2x sqrt(v^(2)-1)`
` rArr (dv)/(2sqrt (v^(2)-1)) = (dx)/x,` integrating ,we get
` rArr 1/2 In (v + sqrt(v^(2)-1))= In Cx`
` rArr 1/2 In ( (y + sqrt(y^(2)-x^(2)))/x)= In Cx `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIAL EQUATION-PRACTICE EXERCISE (Exercise 2 )
  1. The solution of the differential equation x dx + y dy+ (x dy - y d...

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  2. Observe the following statement . I . If dy + 2xy dx = 2e^(-x^(2))...

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  3. The solution of x (dy)/(dx) = y+2 sqrt(y^(2)-x^(2)) is

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  4. Solution of x (dy)/(dx) + y = x^(2) y^(4) is

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  5. The solution of differential equation (dt)/(dx) = (t[d/dx{g(x)}]-...

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  6. The differential equation y(dy)/(dx) + x = c represents

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  7. 8 The solution of differential equation (dy)/(dx)=y/x+(phi(y/x))/(phi'...

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  8. The general solution of (dy)/(dx) = 2x e^(x^(2)-y) is

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  9. The solution of the differential equation (dy)/(dx) = (x(2 log x...

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  10. A solution of y=2x (dy/dx) + x^2(dy/dx)^4 is

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  11. The solution of differential equation (dy)/(dx) + xy = xy^(2) is

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  12. Find the real value of m for which the substitution y=u^m will transfo...

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

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  14. If x^2+y^2=1 then (y'=dy/dx, y''=(d^2y)/dx^2)

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  15. (dy)/(dx)+(3x^2)/(1+x^3)y=(sin^2x)/(1+x^3)

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  16. Solution of the differential equation (dy)/(dx)+ytanx=x^(n)cosx is

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  17. The solution of differential equation (xy^(5)+2y)dx-xdy =0, is

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  18. The solution of the differential equation dy/dx=sin(x+y)+cos(x+y) is:

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  19. The solution of the differential equation x^(4)(dy)/(dx)+x^(3)y+"cosec...

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  20. If the solution of the differential equation (dy)/(dx)=(ax+3)/(2y+f)...

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