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

Lösung

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}}

Schritte zur Lösung

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

Solve linear ODE:

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}}

\int ln (r) d r

y^{^{'}} = - 6 x y^{4}

\frac{d}{d x} (\frac{5 x ^{2} - x}{x})

\int \frac{7 ( x ^{2} + 4 )}{x ( x ^{2} + 7 )} d x

t \to 0 lim (sin (4 t))