Likely exercises: [ y' + a(x) y = b(x) ] Find integrating factor ( \mu(x) = e^{\int a(x) dx} ).
[ \iint_D (x^2 + y^2) , dx, dy ] where ( D = { (x,y) : 0 \le x \le 1,\ 0 \le y \le x } ). Likely exercises: [ y' + a(x) y =
[ y' - 2xy = x ] Solution: integrating factor ( e^{-x^2} ), [ y = e^{x^2} \left( \int x e^{-x^2} dx + C \right) = C e^{x^2} - \frac{1}{2}. ] 2.2 Bernoulli equations [ y' + p(x) y = q(x) y^n ] Substitute ( z = y^{1-n} ). Likely exercises: [ y' + a(x) y =
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