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(1+x^(2))(dy)/(dx)+y=e^(tan^(-1)x)...

`(1+x^(2))(dy)/(dx)+y=e^(tan^(-1)x)`

A

`2ye^(tan-1x)=e^(2tan-1x)+C`

B

`ye^(tan-1x)=e^(2tan-1x)+C`

C

`2ye^(tan-1x)=e^(2tan-1x)+C`

D

None of these

Text Solution

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The correct Answer is:
A
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Solve: (1+x^2) dy/dx+y=e^(tan^-1x)

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Knowledge Check

  • y^(2)-(dy)/(dx)=x^(2)(dy)/(dx) A) y^(-1)+tan^(-1)x=c B) x^(-1)+tan^(-1)y=c C) y+tan^(-1)x=c D) x^(-1)+y^(-1)=tan^(-1)x+c

    A
    `y^(-1)+tan^(-1)x=c`
    B
    `x^(-1)+tan^(-1)y=c`
    C
    `y+tan^(-1)x=c`
    D
    `x^(-1)+y^(-1)=tan^(-1)x+c`

  • The solution of the differential equation (1+y^(2)) dx + (x-e^(-tan^(-1)y) dy = 0 is

    A
    `ye ^(tan^(-1)x ) = tan^(-1) x + C`
    B
    `xe ^(tan^(-1)y ) = tan^(-1) y + C`
    C
    `y = tan^(-1) x e^(tan^(-1)x) +C`
    D
    `y = xe^(tan^(-1)x) + C`

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    e^(-x) (dy)/(dx) = y(1+ tanx + tan^(2) x)

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