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Find the integrating factor of the differential equation x\frac{\mathrm{d} y}{\mathrm{d} x}-2y=2x^2

 

 

 

 
 
 
 
 

Answers (1)

x\frac{\mathrm{d} y}{\mathrm{d} x}-2y=2x^2

\frac{\mathrm{d} y}{\mathrm{d} x}+Py=Q

  then IF=e^{\int Pdx}

\Rightarrow P=\frac{-2}{x}\: \: \: \: Q=2x

     Now          IF=e^{\int \frac{-2}{x}dx}

IF=e^{-2\log x}\Rightarrow e^{\log (x)^{-2}}\: \Rightarrow x^{-2}

\therefore IF=\frac{1}{x^2}

 

Posted by

Ravindra Pindel

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