Matlab 在八度音阶中，有没有一种方法可以用两个变量来解其中一个变量的方程

我有一个MATLAB脚本，它使用拉普拉斯变换求解非齐次一阶线性IVP。（对于本例，设置脚本以解决IVP，）

如果我将“factor”替换为“collect”，脚本几乎可以在八度音阶上工作，符号包链接到SymPy，除了“solve”命令

是否有任何倍频程（或SymPy，如果作为一种解决方法）命令可以作为MATLAB符号工具箱的“solve”命令，这样我就可以用一个脚本通过拉普拉斯变换求解IVP，这样我就不必手动求解X，然后使用“ilaplace”

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提前感谢您提供的任何帮助。

以下是一些倍频程脚本，它们（至少大约）复制了上述MATLAB脚本。您必须在每个脚本的第2部分中手动输入IVP=0的解决方案（根据X），但它们确实起作用。如果有人在MATLAB的solve函数中用X表示八度解IVP=0，我会很高兴听到

这对解算$\dot{x}-3x=t^2$，$x（0）=4$

第1部分：

syms x(t) s X;

a0 = -3;
x0 = 4;
rhs = t^2;

lhs = diff(x,t) + a0*x;
ode = lhs - rhs

Lx = X;
LDx = s*X - x0;
LHS = LDx + a0*Lx;
RHS = laplace(rhs,t,s); % The t and s in laplace aren't necessary, as they are default
IVP = LHS - RHS;

coeff = coeffs(IVP,X);
IVP = coeff*[1;X]

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); % The t and s in laplace aren't necessary, as they are default
IVP = LHS - RHS;

coeff = coeffs(IVP,X);
IVP = coeff*[1;X]

第2部分：

syms x(t) s X;

X = -1*((-4*s^3-2)/s^3)/(s-3)

X = partfrac(X);

sol = ilaplace(X, s, t)
check1 = diff(sol,t) - 3*sol
check2 = vpa(subs(sol, t, 0))

syms x(t) s X;

a1 = -2;
a0 = -3;

X = -1*((-4*s^4 + 3*s^3 - 2)/s^3)/(s^2 - 2*s - 3)

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))

这对解算$\ddot{x}-2\dot{x}-3x=t^2$，$x（0）=4$，$\dot{x}（0）=5$

第1部分：

syms x(t) s X;

a0 = -3;
x0 = 4;
rhs = t^2;

lhs = diff(x,t) + a0*x;
ode = lhs - rhs

Lx = X;
LDx = s*X - x0;
LHS = LDx + a0*Lx;
RHS = laplace(rhs,t,s); % The t and s in laplace aren't necessary, as they are default
IVP = LHS - RHS;

coeff = coeffs(IVP,X);
IVP = coeff*[1;X]

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); % The t and s in laplace aren't necessary, as they are default
IVP = LHS - RHS;

coeff = coeffs(IVP,X);
IVP = coeff*[1;X]

第2部分：

syms x(t) s X;

X = -1*((-4*s^3-2)/s^3)/(s-3)

X = partfrac(X);

sol = ilaplace(X, s, t)
check1 = diff(sol,t) - 3*sol
check2 = vpa(subs(sol, t, 0))

syms x(t) s X;

a1 = -2;
a0 = -3;

X = -1*((-4*s^4 + 3*s^3 - 2)/s^3)/(s^2 - 2*s - 3)

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))

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非常感谢所有的帮助和建议！非常感谢

好的，我的一个学生解决了这个问题（我将在本周晚些时候与他联系，看看他是否希望公开承认他的解决方案）

您只需将

coeff*[1；X]

的结果定义为等于0的方程组，比如

IVPEQ=coeff*[1；X]==0

，然后在此方程上使用符号包命令

solve

，

X=solve（IVPEQ，X）

这是我以前的一阶IVP解算器的一个版本，由我的学生修改

syms x(t) s X;

a0 = -3;
x0 = 4;
rhs = t^2;

lhs = diff(x,t) + a0*x;
ode = lhs - rhs

Lx = X;
LDx = s*X - x0;
LHS = LDx + a0*Lx;
RHS = laplace(rhs,t,s); % The t and s in laplace aren't necessary, as they are default
IVP = LHS - RHS;

coeff = coeffs(IVP,X);
IVPEQ = coeff*[1;X] == 0;

X = solve(IVPEQ,X);

X = partfrac(X);

sol = ilaplace(X, s, t)

Dsol = diff(sol,t);
check1 = Dsol + a0*sol
check2 = vpa(subs(sol, t, 0))

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); % The t and s in laplace aren't necessary, as they are default
IVP = LHS - RHS;

coeff = coeffs(IVP,X);
IVPEQ = coeff*[1;X] == 0;

X = solve(IVPEQ,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))

这是第二阶IVP解算器和学生的修改

syms x(t) s X;

a0 = -3;
x0 = 4;
rhs = t^2;

lhs = diff(x,t) + a0*x;
ode = lhs - rhs

Lx = X;
LDx = s*X - x0;
LHS = LDx + a0*Lx;
RHS = laplace(rhs,t,s); % The t and s in laplace aren't necessary, as they are default
IVP = LHS - RHS;

coeff = coeffs(IVP,X);
IVPEQ = coeff*[1;X] == 0;

X = solve(IVPEQ,X);

X = partfrac(X);

sol = ilaplace(X, s, t)

Dsol = diff(sol,t);
check1 = Dsol + a0*sol
check2 = vpa(subs(sol, t, 0))

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); % The t and s in laplace aren't necessary, as they are default
IVP = LHS - RHS;

coeff = coeffs(IVP,X);
IVPEQ = coeff*[1;X] == 0;

X = solve(IVPEQ,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))

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再次感谢@Tasos_papastylanou，感谢您的大力帮助

你说的“几乎”是什么意思？顺便说一句，

collect

用于收集系数；我在符号包中发现了一个

coefs

函数，它似乎是等效的（尽管在这种情况下，

factor

似乎是有效的），这可能是相关的：非常感谢您的回复！coeffs函数似乎确实符合我的兴趣！用[1；X]进行简单的矩阵乘法可以重现MATLAB的集合。我有一些复制上述MATLAB脚本的半成品脚本（至少大约），但我将在下面的“答案”中发布这些脚本。再次感谢您的回复！