y^{''}+4y^'=2sec^3(2t)

Lösung

y^{^{''}} + 4 y^{^{'}} = 2 sec^{3} (2 t)

y = c_{1} + c_{2} e^{- 4 t} + \frac{sec ( 2 t ) tan ( 2 t ) + ln ( tan ( 2 t ) + sec ( 2 t ) )}{8} + e^{- 4 t} \cdot \int - \frac{sec ^{3} ( 2 t )}{2 e ^{- 4 t}} d t

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) = 2 sec^{3} (2 t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 t} + \frac{sec ( 2 t ) tan ( 2 t ) + ln ( tan ( 2 t ) + sec ( 2 t ) )}{8} + e^{- 4 t} \cdot \int - \frac{sec ^{3} ( 2 t )}{2 e ^{- 4 t}} d t

y = c_{1} + c_{2} e^{- 4 t} + \frac{sec ( 2 t ) tan ( 2 t ) + ln ( tan ( 2 t ) + sec ( 2 t ) )}{8} + e^{- 4 t} \cdot \int - \frac{sec ^{3} ( 2 t )}{2 e ^{- 4 t}} d t

y^{^{''}} - 4 y^{^{'}} = 8 x^{2} + 2 e^{3 x}

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = e^{- 2 x} + 3

x^{^{''}} + 7 x^{^{'}} + 10 x = 20, x (0) = 5, x^{^{'}} (0) = 3

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 x^{2} + 1

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