3/2 (d^2y)/(dx^2)+1/80 (dy)/(dx)=g

解答

\frac{3}{2} \frac{d ^{2} y}{d x ^{2}} + \frac{1}{80} \frac{d y}{d x} = g

y = c_{1} + c_{2} e^{- \frac{x}{120}} + 80 gx

求解步骤

\frac{3}{2} \frac{d ^{2} y}{d x ^{2}} + \frac{1}{80} \frac{d y}{d x} = g

求解线性方程:

y = c_{1} + c_{2} e^{- \frac{x}{120}} + 80 gx

y = c_{1} + c_{2} e^{- \frac{x}{120}} + 80 gx

x^{^{''}} + 2 x^{^{'}} + 5 x = e^{t}

y^{^{''}} + 40 y^{^{'}} + 4000 y = 800 sin (40 x)

y^{^{''}} + y^{^{'}} = e^{x} cos (x)

(d - 1)^{3} y = e^{x} + 5^{x} - 1

y^{^{''}} - 2 y^{^{'}} + y = 12 e^{3 t}, y (0) = - 1, y^{^{'}} (0) = 0