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The solution of the differential equatio...

The solution of the differential equation
` y - x ( dy)/(dx) = a ( y^(2) + dy/dx)` is

A

`y = C (x+a)(1-ay)`

B

`y = C( x+a) (1+ay)`

C

`y = C(x-a)(1+ay)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
d
Given , ` y - x (dy)/(dx) = a (y^(2) +dy/dx)`
` rArr (dy)/(dx) (a+x) = y - ay^(2) `
On integrating both sides , we get
` rArr int (1/y +a/(1-ay))dy = int (dx)/(a+x)`
` rArr log y - log (1-ay) = log (a+x) +log C`
` rArr log y = log (1- ay) (a+x)C`
` rArr y = C ( 1-ay ) (a+x)`
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Knowledge Check

  • The solution of the differential equation x(dy)/(dx)+y = y^2 is

    A
    y=1+cxy
    B
    y=log (cxy)
    C
    y+1 = cxy
    D
    y=c+xy

  • The solution of the differential equation (x+y)^2(dy)/(dx)=a^2 is

    A
    `(x+y)^2=(dy)/(dx)=(a^2x)/2+C`
    B
    `(x+y)^2=a^2 x+C`
    C
    `(x+y)^2=2a^2x+C`
    D
    None of the above

  • The solution of the differential equation (x - y) dy - (x + y) dx =0, is

    A
    `tan^(-1)"" (x)/(y) + (1)/(2) log (x^(2) + y^(2)) = C`
    B
    ` tan^(-1)"' (y)/(x) - (1)/(2) log(x^(2) + y^(2)) = C`
    C
    `cot^(-1)"" ((y)/(x)) + (1)/(2) log (x^(2) + y^(2) = C`
    D
    None of the above

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