y^{''}+2y^'-3y=x^2sin(x)

解答

y^{^{''}} + 2 y^{^{'}} - 3 y = x^{2} sin (x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( x )}{5} - \frac{x ^{2} cos ( x )}{10} + \frac{x sin ( x )}{25} - \frac{7 x cos ( x )}{25} + \frac{29}{250} sin (x) - \frac{14}{125} cos (x)

求解步骤

y^{''} (x) + 2 y^{'} (x) - 3 y = x^{2} sin (x)

求解线性方程:

y = c_{1} e^{x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( x )}{5} - \frac{x ^{2} cos ( x )}{10} + \frac{x sin ( x )}{25} - \frac{7 x cos ( x )}{25} + \frac{29}{250} sin (x) - \frac{14}{125} cos (x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} - \frac{x ^{2} sin ( x )}{5} - \frac{x ^{2} cos ( x )}{10} + \frac{x sin ( x )}{25} - \frac{7 x cos ( x )}{25} + \frac{29}{250} sin (x) - \frac{14}{125} cos (x)

y^{^{''}} + 5 y = - 9.81

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 e^{- 3 x}

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = x e^{3 x}

y^{^{'''}} - 4 y^{^{''}} + 4 y^{^{'}} = x^{2} - e^{2 x}

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- t}