The integrating factor of the differential equation $straight x dy over dx minus straight y space equals space 2 straight x squared$ is

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Solution

The given differential equation is

straight x dy over dx minus straight y space equals 2 straight x squared space space space space space or space space space dy over dx minus 1 over straight x straight y space equals 2 straight x

Comparing it with

dy over dx plus Py space equals space straight Q comma space space we space get comma space straight P space equals space minus 1 over straight x comma space space straight Q space equals space 2 straight x

I.F. =

straight e to the power of integral straight P space dx end exponent space equals space straight e to the power of negative integral space 1 over straight x dx end exponent space equals space straight e to the power of negative space log space straight x end exponent space equals space straight e to the power of log space straight x to the power of negative 1 end exponent end exponent space equals space straight x to the power of negative 1 end exponent space equals space 1 over straight x

therefore space space space left parenthesis straight C right parenthesis space is space correct space answer.

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