(dy)/(dt)=sin(2pi(t+3))

解答

\frac{d y}{d t} = sin (2 π (t + 3))

y = - \frac{1}{2 π} cos (2 π (t + 3)) + c_{1}

求解步骤

\frac{d y}{d t} = sin (2 π (t + 3))

替代

\frac{d y}{d t}

与

y^{'} (t)

y^{^{'}} (t) = sin (2 π (t + 3))

若

f^{^{'}} (x) = g (x)

则

f (x) = \int g (x) d x

y = \int sin (2 π (t + 3)) d t

\int sin (2 π (t + 3)) d t = - \frac{1}{2 π} cos (2 π (t + 3)) + c_{1}

y = - \frac{1}{2 π} cos (2 π (t + 3)) + c_{1}

t a y l or e^{3 x}

x (\frac{d y}{d x}) = 4 y

l a pl a ce t r an s f or m {6 e^{- 3 t} - t^{2} + 2 t - 8}

(y - x) e^{x} + (1 + e^{x}) \frac{d y}{d x} = 0

\int_{0}^{1} 2 π x (x - x) d x