y^{''}-a^2y=sec(ax)

Lösung

y^{^{''}} - a^{2} y = sec (a x)

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

Schritte zur Lösung

y^{''} (x) - a^{2} y = sec (a x)

Solve linear ODE:

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

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

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

y^{^{''}} + 2 y^{^{'}} + 2 y = t^{2}, y (0) = \frac{1}{2}, y^{^{'}} (0) = 0

y^{^{'''}} + 265 y^{^{'}} = tan (16 x)

y^{^{''}} - 10 y^{^{'}} + 9 y = e^{2 x}

y^{^{''}} + y^{^{'}} - 6 y = e^{2 t} + t