3= pi/(12) d/(dt)((h(t))^3)

解答

3 = \frac{π}{12} \frac{d}{d t} ((h (t))^{3})

h (t) = 3 \frac{36 t + c _{1}}{π}, h (t) = - \frac{π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π} + i \frac{3 π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π}, h (t) = - \frac{π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π} - i \frac{3 π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π}

求解步骤

3 = \frac{π}{12} \frac{d}{d t} ((h (t))^{3})

整理

(h (t)^{3})^{'} : (h (t)^{3})^{'} = \frac{36}{π}

若

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

则

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

h (t)^{3} = \int \frac{36}{π} d t

\int \frac{36}{π} d t = \frac{36}{π} t + c_{1}

h (t)^{3} = \frac{36}{π} t + c_{1}

整理

h (t) : h (t) = 3 \frac{36 t + π c _{1}}{π}, h (t) = - \frac{π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π} + i \frac{3 π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π}, h (t) = - \frac{π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π} - i \frac{3 π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π}

h (t) = 3 \frac{36 t + π c _{1}}{π}, h (t) = - \frac{π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π} + i \frac{3 π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π}, h (t) = - \frac{π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π} - i \frac{3 π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π}

化简

h (t) = 3 \frac{36 t + c _{1}}{π}, h (t) = - \frac{π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π} + i \frac{3 π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π}, h (t) = - \frac{π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π} - i \frac{3 π ^{\frac{2}{3}} 3 36 t + π c _{1}}{2 π}

2 sin (3 x) sin (2 y) d y = 3 cos (3 x) cos (2 y) d x

7 x y \frac{d y}{d x} = 3, y > 0, x > 0

\frac{d x}{d t} + \frac{8 x}{240} = 2

\frac{d y}{d x} = 4 x - 7 x y

y^{^{'}} y = (x^{2} - 2 x + 2) (4 x^{3} - x^{2} + 5)