y^{''}-y= 1/(cosh(x))

Lösung

y^{^{''}} - y = \frac{1}{cosh ( x )}

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

Schritte zur Lösung

y^{''} (x) - y = \frac{1}{cosh ( x )}

Solve linear ODE:

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

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

x^{^{''}} + 2 x^{^{'}} + x = e^{- 2 t}, x (0) = 2

y^{^{''}} + 4 y^{^{'}} + 13 y = cos (3 x)

4 y^{^{''}} - y = sin (x)

y^{^{''}} + 4 y^{^{'}} + 4 y = 6 x + 7

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = sin (3 x)