y^{''}+y^'+1.25y=3cos(x)

解答

y^{^{''}} + y^{^{'}} + 1.25 y = 3 cos (x)

y = e^{- \frac{x}{2}} (c_{1} cos (x) + c_{2} sin (x)) + 2.82352 \dots sin (x) + 0.70588 \dots cos (x)

求解步骤

y^{''} (x) + y^{'} (x) + 1.25 y = 3 cos (x)

求解线性方程:

y = e^{- \frac{x}{2}} (c_{1} cos (x) + c_{2} sin (x)) + 2.82352 \dots sin (x) + 0.70588 \dots cos (x)

y = e^{- \frac{x}{2}} (c_{1} cos (x) + c_{2} sin (x)) + 2.82352 \dots sin (x) + 0.70588 \dots cos (x)

y^{^{''}} = 9 + (y^{^{'}}) 2

y^{^{''}} + 6 y^{^{'}} - 27 y = - 105 t + 54 t^{2}

y^{^{''}} - 6 y^{^{'}} + 5 y = x, y^{1} (0) = e^{x}

y^{^{''}} - 6 y + 9 y = e^{3 x}

y^{^{''}} + 4 y = 3 csc^{2} (2 x)