Q21 of 45 Page 1

Find the particular solution of the following differential equation:

when x = 1

The given differential equation is … (1)


Separating given differential equation, we get



On integrating, we get





⇒ y – 2 log (y + 2) = x + 2 log x + C ... (2)


Putting y = -1, when x = 1 in (2), we get


⇒ -1 – 2 log 1 = 1 + 2 log 1 + C


⇒ -1 – 0 = 1 + 0 + C


∴ C = -2


Equation (2) becomes y – 2 log (y + 2) = x + 2 log x – 2


⇒ y – x + 2 = 2 [log x + log (y + 2)]


⇒ y – x + 2 = 2 log {x (y + 2)}


∴ The required solution is y – x + 2 = 2 log {x (y + 2)}


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