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

Lösung

5 y^{^{''}} - 10 y^{^{'}} + 10 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 )}{5}

Schritte zur Lösung

5 y^{''} (x) - 10 y^{'} (x) + 10 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 )}{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^{^{'}} + y = \frac{e ^{x}}{x ^{2}}

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

y^{^{'''}} + y^{^{''}} + 4 y^{^{'}} + 4 y = 100 x sin (3 x)

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 x} ln (1 + x^{2})

y^{^{''}} + y^{^{'}} - 6 y = e^{- 3 x}