y^{''}+y^'=sec(t)

Lösung

y^{^{''}} + y^{^{'}} = sec (t)

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

Schritte zur Lösung

y^{''} (t) + y^{'} (t) = sec (t)

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} + y = - 1

y^{^{''}} + 4 y = (sin (x))^{2}

x^{^{''}} + x^{^{'}} + 4 = 0

y^{^{''}} + 4 y = (sin (x))^{3}

4 y^{^{''}} + 5 y^{^{'}} + 2 y = - 2 x^{2} + x