一些常见的凑微分形式 ·对f'(x)=f(x),构造g(x)=f(x)e-e. ·对f'(x)+f(x)=入，构造g(x)=(f(x)-入)e2. ·对f'(x)-A(f(x)-x)=1,构造g(x)=(f(x)-x)e- ·对xf'(x)+af(x)=0,构造g(x)=xf(x). ·对xf(r)+f'(x)=0,构造g(x)=f(x)er2. ·对"(x)+f(x)=0,构造g(x)=P(x)+(f'(x)2. ·对f"(x)=f(x),构造g(x)=(f'(x)+f(x)e-x或g(x)=(f'(x)-f(x)e. 1
一些常见的凑微分形式 • 对 f ′ (x) = f(x), 构造 g(x) = f(x)e −x . • 对 f ′ (x) + f(x) = λ, 构造 g(x) = (f(x) − λ)e x . • 对 f ′ (x) − λ(f(x) − x) = 1, 构造 g(x) = (f(x) − x)e −λx . • 对 xf′ (x) + αf(x) = 0, 构造 g(x) = x α f(x). • 对 xf(x) + f ′ (x) = 0, 构造 g(x) = f(x)e x 2/2 . • 对 f ′′(x) + f(x) = 0, 构造 g(x) = f 2 (x) + (f ′ (x))2 . • 对 f ′′(x) = f(x), 构造 g(x) = (f ′ (x) + f(x))e −x 或 g(x) = (f ′ (x) − f(x))e x . 1