5y^{''}-10y^'+10y=e^x*sec(x)

Lösung

5 y^{^{''}} - 10 y^{^{'}} + 10 y = e^{x} \cdot 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 )}{5}

Schritte zur Lösung

5 y^{''} (x) - 10 y^{'} (x) + 10 y = e^{x} \cdot 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 )}{5}

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e ^{x} ln ( cos ( x ) ) cos ( x ) + e ^{x} x sin ( x )}{5}

y^{^{''}} - 2 y^{^{'}} + 2 y = e x sin (x)

y^{^{''}} + 6 y^{^{'}} + 5 y = e^{x}

y^{^{''}} + 5 y^{^{'}} + 6 = sin (x) - cos (2 x)

y^{^{'''}} - y^{^{'}} = e^{(x)} + e^{(2 x)}

y^{^{'''}} - 6 y^{^{''}} + 25 y^{^{'}} = 68 e^{2 x}