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The solution of (dy)/(dx) = 1+ y + y^(2...

The solution of ` (dy)/(dx) = 1+ y + y^(2) + x+ xy + xy^(2)` is

A

`2/sqrt3tan^(-1)((2y+1)/sqrt3)=x+x^2+c`

B

`4tan^(-1)((2y-1)/sqrt3)=sqrt3/2 (2x+x^2) +c `

C

`sqrt3tan^(-1)((3y+1)/sqrt3)=4(1+x+x^2)+c`

D

`4 tan^(-1)((2y+1)/sqrt3)=sqrt3(2x+x^2)+c`

Text Solution

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The correct Answer is:
D
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TARGET PUBLICATION-DIFFERENTIAL EQUATIONS -COMPETITIVE THINKING
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  2. The general solution of the differential equation (dy)/(dx)+sin(x+y)/2...

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  3. The solution of (dy)/(dx) = 1+ y + y^(2) + x+ xy + xy^(2) is

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  4. The solution of the differential equation (dy)/(dx)=3^(x+y) at x=0=y i...

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  5. The particular solution of the differential equation xdy + 2 y dx = ...

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  6. The solution of the differential equation 2x(dy)/(dx)-y=0 , y(1)=2 re...

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  7. Particular solution of differential equation e^("dy"/"dx") =x:y (1) = ...

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  8. The solution of log.(dy)/(dx)=x when y=1 and x=0 is :

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  9. Find the particular solution of the differential equation log(dy)/(...

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  10. If (dy)/(dx)=y+3 and y(0)=2, then y(ln 2) is equal to

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  11. If "dy"/"dx"=1-y and y(0)=3, then y(loge 8) is equal to

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  12. The particular solution of the differential equation y(1+log x...

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  13. Solution of the differential equation sin((dy)/(dx))=a with y(0)=1 is

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  14. if y=y(x) and (2+sinx)/(y+1)((dy)/(dx))=-cosx ,y(0)=1, then y(pi/2)= ...

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  15. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

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  16. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

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  17. At any point on a curve , the slope of the tangent is equal to the sum...

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  18. The general solution of the D.E. (dy)/(dx)=(x+y+1)/(x+y-1) is :

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  19. solution of (x + y)^2(dy)/(dx)=a^2. ('a', being a constant) is

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  20. Solution of the differential equation (x+y-1)dx+(2x+2y-3)dy=0 is

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