y^{''}-y=sec^3(x)-sec(x)

Lösung

y^{^{''}} - y = sec^{3} (x) - sec (x)

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

Schritte zur Lösung

y^{''} (x) - y = sec^{3} (x) - sec (x)

Solve linear ODE:

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

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

y^{^{''''}} - 5 y^{^{''}} + 4 y = 8 cos (2 x) - 12 e^{- x}

x^{^{''}} + x = 9 cos (8 t)

y^{^{''}} + y = - sec (x)

y^{^{''}} + \frac{53}{7} \cdot y^{^{'}} + 49 x = 0

D (f (x)) = 4 sec (4 x) tan (4) (x)