(dy)/(dt)y=(4t-1)(3t-6)^{-1}

解

\frac{d y}{d t} y = (4 t - 1) (3 t - 6)^{- 1}

y = \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}, y = - \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}

解答ステップ

\frac{d y}{d t} y = (4 t - 1) (3 t - 6)^{- 1}

分離可能 ODE を解く:

y = \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}, y = - \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}

y = \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}, y = - \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}