如何修复 'Equations may not give solutions for all "solve" variables' 错误

Question

我正在尝试一个可以用 MUC（待定系数法）解决的问题。

但是，当我使用 Solve 函数时，出现错误。

y[x_] := a x^3 + b x^2 + c x + d
Solve[{y''[x] + 2 y'[x] + y[x] == x^3}, {a, b, c, d}]

[ERROR]:
Solve::svars: Equations may not give solutions for all "solve" variables.

这不应该解决集合中的所有变量吗？

感谢您的帮助:)

Answer 1

看起来 some extra methodology 需要这样做。

正如您所说，x^3 的有限导数族的函数是

y[x_] := a x^3 + b x^2 + c x + d

等化系数

sol = Solve[Thread[CoefficientList[
     y''[x] + 2 y'[x] + y[x], x] == CoefficientList[x^3, x]]]

{{a -> 1, b -> -6, c -> 18, d -> -24}}

检查结果

FullSimplify[y''[x] + 2 y'[x] + y[x] == x^3 /. sol]

{True}

如何修复 'Equations may not give solutions for all "solve" variables' 错误

How to fix 'Equations may not give solutions for all "solve" variables' error

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