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**Unformatted text preview: **= 1 e 4 y + 2 x is, clearly, not linear. But, if we switch the roles of variables and consider y as the independent variable and x as the dependent variable (using the connection between derivatives of inverse functions, that is, the formula y ( x ) = 1 /x ( y )), then the equation transforms to dx dy = e 4 y + 2 x dx dy 2 x = e 4 y . This is a linear equation with P ( y ) = 2. Thus the integrating factor is ( y ) = exp Z ( 2) dy = e 2 y 51...

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