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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} - 10 y^{^{'}} + 25 y = 10 e^{5 x}

2 x^{^{''}} + 4 x = 6 t

y^{^{''}} + 3 y^{^{'}} + 2 y = 18 + e x

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

y^{^{''}} - 25 y = e^{5 t}