y^{''}-8y^'+16y=10e^{4x}sec(x)

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = 10 e^{4 x} sec (x)

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + e^{4 x} \cdot \int - 10 x sec (x) d x + 10 e^{4 x} x ln (tan (x) + sec (x))

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 16 y = 10 e^{4 x} sec (x)

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + e^{4 x} \cdot \int - 10 x sec (x) d x + 10 e^{4 x} x ln (tan (x) + sec (x))

y = c_{1} e^{4 x} + c_{2} x e^{4 x} + e^{4 x} \cdot \int - 10 x sec (x) d x + 10 e^{4 x} x ln (tan (x) + sec (x))

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

y^{^{''}} + 4 y^{^{'}} + 6 y = 1 + e^{- t}

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

y^{^{''}} - 3 y^{^{'}} + 2 y = sin (t)

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