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Unformatted text preview: f ( x ). To do that use the following results in previous question Q ( x ) = P ( x ) + f ( x ) and R ( x ) = f ( x ) The rst equation implies that f ( x ) = Q ( x )-P ( x ) = x-0 = x . Hence, the dierential equation can be written as [ y ] + [ xy ] = 0 which is the same as [ y + xy ] = 0 Integrating this equation once, we get y + xy = c 1 Iit is now a rst order linear dierential equation. Use integrating factor method to solve this equation for y. = e R xdx = e x 2 / 2 then ( e x 2 / 2 y ) = c 1 e x 2 / 2 . Integrating this you get, e x 2 / 2 y = R c 1 e x 2 / 2 dx + c 2 Thus the solution is y = 1 e x 2 / 2 Z c 1 e x 2 / 2 dx + c 2...
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