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The Integrating Factor of the different...

The Integrating Factor of the differential equation `x(dy)/(dx)-y=2x^2`is(A) `e^(-x)` (B) `e^(-y)` (C) `1/x` (D) x

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To find the integrating factor of the differential equation \( x \frac{dy}{dx} - y = 2x^2 \), we will follow these steps: ### Step 1: Rewrite the differential equation in standard form The given equation is: \[ x \frac{dy}{dx} - y = 2x^2 \] We can rearrange it to the standard linear form: ...
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Knowledge Check

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

    A
    `e^(x+y+2)`
    B
    `e^y`
    C
    `e^(-y)`
    D
    log |x+y+2|

  • The integrating factor of the differential equation x.(dy)/(dx)+2y=x^2 is ( x ne 0 )

    A
    `x^2`
    B
    log |x|
    C
    `e^(log x)`
    D
    x

  • The integrating factor of the differential equation (dy)/(dx)+y=(1+y)/(x) , is

    A
    `(x)/(e^(x))`
    B
    `(e^(x))/(x)`
    C
    `xe^(x)`
    D
    `e^(x)`

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