x^'+(2sin(t)cos(t))x=e^{-sin^2(t)}

解

x^{^{'}} + (2 sin (t) cos (t)) x = e^{- s i n^{2} (t)}

x = \frac{t}{e e ^{- \frac{c o s ( 2 t )}{2}}} + c_{1} e^{\frac{c o s ( 2 t )}{2}}

解答ステップ

x^{'} (t) + (2 sin (t) cos (t)) x = e^{- s i n^{2} (t)}

線形 ODE を解く:

x = \frac{t}{e e ^{- \frac{c o s ( 2 t )}{2}}} + c_{1} e^{\frac{c o s ( 2 t )}{2}}

x = \frac{t}{e e ^{- \frac{c o s ( 2 t )}{2}}} + c_{1} e^{\frac{c o s ( 2 t )}{2}}