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The solution of the differential equatio...

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

A

`2xe^(tan^(-1)y)=e^(2tan^(-1)y)+k`

B

`xe^(tan^(-1)y)=tan^(-1)y+k`

C

`xe^(2tan^(-1)y)=e^(tan^(-1)y)+k`

D

`(x-2)=ke^(-tan^(-1)y)`

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A
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The solution of differential equation (1+y^(2))+((x-2e^(tan^(-1)y))dy)/(dx)=0 is (x-2)=ke^(tan^(-1)y)xe^(tan-1)y=e^(2)tan^(-4)y+kxe^(tan^(-1)y)=tan^(-1)y+kxe^(2tan^(-1)y)=e^(2tan^(-1)y)+k

The solution of the differential equation (1+y^2)+(x-e^(tan^-1y))dy/dx=0 is (A) x e^(2 tan^-1y)=e^(tan^-1y)+k (B) (x-2)=k e^(-tan^-1y) (C) x e^(tan^-1y)=e^(2 tan^-1y)+k (D) x e^(tan^-1y)=tan^-1y+k

Knowledge Check

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

    A
    `(x-2)=ke^(-tan^(-1)y)`
    B
    `2x e^(tan^(-1)y)=e^(2tan^(-1)y)+k`
    C
    `x e^(tan^(-1)y)=tan^(-1)y+k`
    D
    `x e^(2tan^(-1)y)=e^(tan^(-1)y)+k`

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

    A
    `2xe^(tan^(-1)y)=e^(2tan^(-1)y)+k`
    B
    `2xe^(tan^(-1)y)=e^(tan^(-1)y)+k`
    C
    `xe^(tan^(-1)y)=e^(tan^(-1)y)+k`
    D
    `xe^(tan^(-1)y)`

  • 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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