4y^{''}-8y^'+8y=e^xsec(x)

Lösung

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

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e ^{x} ln ( cos ( x ) ) cos ( x ) + e ^{x} x sin ( x )}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e ^{x} ln ( cos ( x ) ) cos ( x ) + e ^{x} x sin ( x )}{4}

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e ^{x} ln ( cos ( x ) ) cos ( x ) + e ^{x} x sin ( x )}{4}

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{e ^{x} + 1}

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{x}}{x ^{2} + 1}

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

2 y^{^{''}} + y^{^{'}} - y = x + 7, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} = 6 e^{3 t} - 3 e^{- t}