f^'(x)+2xf(x)=0,f(0)=3

解答

f^{^{'}} (x) + 2 x f (x) = 0, f (0) = 3

f (x) = 3 e^{- x^{2}}

求解步骤

f^{'} (x) + 2 x f (x) = 0

求解可分离方程:

f (x) = 3 e^{- x^{2}}

f (x) = 3 e^{- x^{2}}

- 2 y \frac{d y}{d x} + x^{2} + 2 x^{4} = 0

4 y \frac{d y}{d x} = x + x y^{2}

y^{^{'}} sin (2 y) - cos (x) = 0

\frac{df}{d t} = f (t)

y^{^{'}} + ln (x) \cdot y = 3 \cdot ln (x)