y^{'''}-y^'=csc(t)

解

y^{^{'''}} - y^{^{'}} = csc (t)

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} - ln (tan (\frac{t}{2})) + e^{- t} \cdot \int \frac{e ^{t} csc ( t )}{2} d t + e^{t} \cdot \int \frac{e ^{- t} csc ( t )}{2} d t

解答ステップ

y^{'''} (t) - y^{'} (t) = csc (t)

線形 ODE を解く:

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} - ln (tan (\frac{t}{2})) + e^{- t} \cdot \int \frac{e ^{t} csc ( t )}{2} d t + e^{t} \cdot \int \frac{e ^{- t} csc ( t )}{2} d t

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} - ln (tan (\frac{t}{2})) + e^{- t} \cdot \int \frac{e ^{t} csc ( t )}{2} d t + e^{t} \cdot \int \frac{e ^{- t} csc ( t )}{2} d t