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

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

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Knowledge Check

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

    A
    `tan^(-1)x`
    B
    `1+x^2`
    C
    `e^(tan^(-1)x)`
    D
    `log_e (1+x^2)`

  • The integrating factor of the differential equation (1+x^2)(dy)/(dx)+y=e^("tan"^(-1)x) is

    A
    `tan^(-1)x `
    B
    `1+x^2`
    C
    `e^("tan"^(-1)x)`
    D
    `log(1+x^2)`

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

    A
    `ye^(tan^(-1)x) = (1)/(2)e^(2tan^(-1)x) + C`
    B
    `y = (1)/(2)e^(2 tan^(-1)x) + C`
    C
    `ye^(tan^(-1)x) = 2e^(2 tan^(-1)x) + C`
    D
    `y. tan^(-1) x = (1)/(2) e^(2 tan^(-1)x) + C`

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