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Unformatted text preview: the standard procedure, in standard form this is dy dx + 1 1 + x y = cos x 1 + x . So a ( x ) = 1 / (1 + x ), A ( x ) = R a ( x ) dx = ln | 1 + x | and the integrating factor is e A = | 1+ x | = (1+ x ). Either one will work. Using +(1+ x ), you get back to the original equation! So you have (1 + x ) dy dx + y = cos x, d dx (1 + x ) y = cos x, (1 + x ) y = sin x + C. So the general solution is y ( x ) = sin x 1 + x + C 1 + x ....
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