我有一个.m脚本，用于在MATLAB中使用具有常系数的非齐次一阶线性IVP;我将使用$ \ dot {x} - 3x = t ^ 2 $，$ x（0）= 4 $作为示例：
syms x(t) s X
Dx = diff(x(t),t)
ode = Dx - 3*x - t^2
x0 = 4
ODE = laplace(ode,t,s) % The t and s in laplace aren't necessary, as they are default
IVP = subs(ODE,{x(0)},{x0})
IVP = subs(IVP,{laplace(x(t),t,s)},{X})
IVP = collect(IVP,X)
X = solve(IVP, X)
X = partfrac(X)
sol = ilaplace(X, s, t)
Dsol = diff(sol,t)
check1 = Dsol - 3*sol
check2 = vpa(subs(sol, t, 0))
工作正常。
当我尝试对具有常系数的二阶线性IVP执行此脚本的变体时，我会在t = 0时尝试替换一阶导数的值（使用$ \ ddot {x} - 2 \ dot {x} - 3x = t ^ 2 $，$ x（0）= 4 $，$ \ dot {x} = 5 $为例）：
syms x(t) s X
Dx = diff(x,t)
D2x = diff(x, t, 2)
ode = D2x - 2*Dx - 3*x - t^2
x0 = 4
xdot0 = 5
ODE = laplace(ode,t,s)
IVP = subs(ODE,{x(0)},{x0})
IVP = subs(ODE,{D(x)(0)},{xdot0}) % <- <- THIS IS THE PROBLEM LINE!!
IVP = subs(IVP,{laplace(x(t),t,s)},{X})
IVP = collect(IVP,X)
X = solve(IVP, X)
X = partfrac(X)
sol = ilaplace(X, s, t)
Dsol = diff(sol,t)
D2sol = diff(sol, t, 2)
check1 = D2sol - 2*Dsol - 3*sol
check2 = vpa(subs(sol, t, 0))
check3 = vpa(subs(Dsol, t, 0))
我不确定在二阶导数的拉普拉斯变换中作为变量D（x）（0）放置什么;我尝试的一切都给了我一些错误或其他错误。我不得不求助于kludgy
syms x(t) s X
a1 =-2
a0 = -3
x0 = 4
xdot0 = 5
rhs = t^2
Dx = diff(x,t)
D2x = diff(x,t,2)
lhs = D2x + a1*Dx + a0*x
ode = lhs - rhs
Lx = X
LDx = s*X - x0
LD2x = s^2*X - x0*s - xdot0
LHS = LD2x + a1*LDx + a0*Lx
RHS = laplace(rhs,t,s)
IVP = LHS - RHS
IVP = collect(IVP,X)
X = solve(IVP, X)
X = partfrac(X)
sol = ilaplace(X, s, t)
Dsol = diff(sol,t)
D2sol = diff(sol,t,2)
check1 = D2sol + a1*Dsol + a0*sol
check2 = vpa(subs(sol, t, 0))
check3 = vpa(subs(Dsol, t, 0))
使用here的建议。我真正需要知道的是＆＃34; D（x）（0）＆＃34;。我试过D（x）（0）＆＃39;，diff（x，t）（0），Dx（0），
help = D(x)
IVP = subs(ODE,{help(0)},{xdot0})
help2 = diff(x,t)
IVP = subs(ODE,{help2(0)},{xdot0})
你说出来，没有任何效果。
提前感谢您提供的任何帮助。