用Mathematica的 DSolve 解微分方程时返回True的原因和解决办法

我遇到这个问题后在网上找到了答案，网上原文如下：

Question: DSolve returns true

Using Mathematica 7, I got a solution

(* Commands 1*) Clear[x, y]; DSolve[ y'[x] == x - y[x], y[x], x] {{y[x] -> -1 + x + E^-x C[1]}}

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(* Commands 1*)     Clear[x, y]; DSolve[ y'[x] == x - y[x], y[x], x] {{y[x] -> -1 + x + E^-x C[1]}}

The only time I was able to reproduce the “DSolve[True….” message was when I had the sequence of commands as follows,

Clear[x, y]; y'[x] = x - y[x]; DSolve[y'[x] == x - y[x], y[x], x]

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Clear[x, y]; y'[x] = x - y[x]; DSolve[y'[x] == x - y[x], y[x], x]

What’s happening is that y'[x] is known to be x- y[x], and the DSolve is doing a compare of y-y[x] == y-y[x], returning True. Then it can’t solve True for y[x] in x, resulting in the question being returned.

Would you try exiting the kernel, restart fresh, and re-typing (* commands 1*) only.

 

（内容出自 Wolfram Community http://community.wolfram.com/groups/-/m/t/332674）

意思就是，在DSolve解方程时，已事先给出了 y‘[x] 解析表达式，后来又来 y'[x] == x – y[x] 后，相当于在这里比较真假，因此返回 True。

解决办法：删去事先给出的f[x]表达式，清理内存，或者关掉从头重新计算，建议采用后一种方法，比较快速稳妥。