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

解

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}

解答ステップ

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

線形 ODE を解く:

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}