Trying to type up my "cheat sheet":
1. Class: type, order, lin. Lin if != yy’, y’^n (n >1), sin (y). 2. Hmg: f(tx, ty) = t^n f(x,y). Use y = ux or x = vy, then separation of variables, and then sub back. 3. Exact eq: cd = partial. cdM/cd y = cdN/ cd x cdf/cd x = M f = int M + g(y) cdf/cd y = N N = cdM/cd y, solve for g’(y) and int.
4.Lin. eq. dy/dx + P(x)y = f(x). Divide by Ao, use u(x) = e^ (int P(x) dx.) Times eq by IF d/dx[IF * y] = IF * f(x). Integrate both sides and solve for y. 5. Bernoulli’s equation. Similar to 4., but…Divide by y^n. Make sub w = y^1-n. Take dw/dx. Find IF. Multiply thru all factors. Int the dw/dx[IF * w] = IF * f(x).
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