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Using the substitution x + y = u : (1)...

Using the substitution x + y = u :
(1) ` (x+ y)dy = a^(2) dx`

Text Solution

Verified by Experts

The correct Answer is:
`x+y+a^(2) =c.e^(y//a^(@))`
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Knowledge Check

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

    A
    `y = x tan ((x^(2) + y^(2) + C)/(2))`
    B
    `x = y tan ((x^(2) + y^(2) + C)/(2))`
    C
    `y = x tan ((C - x^(2) - y^(2))/(2))`
    D
    None of these

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

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

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    Find the real value of m for which the substitution y=u^(m) will transform the differential equation 2x^(4)y(dy)/(dx)+y^(4)=4x^(6) in to a homogeneous equation.

    The real value of m for which the substitution y =u^m will transform the differential equation 2x^4*y(dy)/(dx)+y^4=4x^6 into a homogeneous equation, is

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