MATH201 Lecture 3: 3. Exact Equations.pdf
18 Jun 2015
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General solution: linear equations, how to solve: H(y) = g(x) + c; y = ci for ci. S satisfying p(ci) = 0. a1(x) dy dx. + a0(x) y = b(x): write the equation into standard form dy dx. We see that this can be done by dividing both sides by a1(x): compute. To be sure your integrating factor is correct, check. (x) = er p (x): the general solution is then d dx. (x: check solution if time allows, quiz: solve (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) + 2 x y = 1(cid:20) x2 y = x + c(cid:20) y = (x) = exp(cid:20) z p (x) dx(cid:21)= exp [2 ln |x|] = exp (ln x2) = x2. Multiply the equation by (x) (note that must multiply the standard form equation, not the original one! d dx (x2 y) = x2 dy dx.
