(dh}{dt}=\frac{(7-e^{-t/5}))/6-2/9 h

解

\frac{d h}{d t} = \frac{( 7 - e ^{- \frac{t}{5}} )}{6} - \frac{2}{9} h

h = \frac{3 ( 7 e ^{\frac{2 t}{9}} - 10 e ^{\frac{t}{45}} )}{4 e ^{\frac{2 t}{9}}} + \frac{c _{1}}{e ^{\frac{2 t}{9}}}

解答ステップ

\frac{d h}{d t} = \frac{( 7 - e ^{- \frac{t}{5}} )}{6} - \frac{2}{9} h

線形 ODE を解く:

h = \frac{3 ( 7 e ^{\frac{2 t}{9}} - 10 e ^{\frac{t}{45}} )}{4 e ^{\frac{2 t}{9}}} + \frac{c _{1}}{e ^{\frac{2 t}{9}}}

h = \frac{3 ( 7 e ^{\frac{2 t}{9}} - 10 e ^{\frac{t}{45}} )}{4 e ^{\frac{2 t}{9}}} + \frac{c _{1}}{e ^{\frac{2 t}{9}}}