Find the Integerating Factor of the Differential Equation X D Y D X − 2 Y = 2 X 2 . - Mathematics

Sum

Find the integerating factor of the differential equation xdy/dx - 2y = 2x^2 .

Solution

dy/dx + (-2/x)y = 2x

compare with dy/dx + py = Q

⇒ p = -2/x

therefore Integrating factor IF = e^(∫pdx)

= e^(∫-2/xdx)

= e^(-2"In "x)

= e^("In"  x^-2)

= x^-2

= 1/x^2

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