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# (M4+)Using differentiation to show that x is a solution for the differential equation watch

1. This question is from M5, however it can be relevant to other modules and exam boards, hence the M4+ in the title.

So when I saw part (b), my laziness immediately made me think of just differentiating the given and showing that is equal to , by substituting of course. That way I don't have to do that semi-messy integral that I'll probably get from the differential equation in part (a).

However, knowing the stupidity of some mark schemes, I'm a bit wary of using this in an actual exam. What do you think?
2. Granted that mark schemes can be silly however a substitution will serve for a "show that " question. In fact, show that is a hint that this is what is required.
3. (Original post by nerak99)
Granted that mark schemes can be silly however a substitution will serve for a "show that " question. In fact, show that is a hint that this is what is required.
In the solutions they actually solved the differential equation, using integration (which required a substitution, surprisingly!). However these solutions aren't like mark schemes, so you're probably right.
4. (Original post by gagafacea1)
In the solutions they actually solved the differential equation, using integration (which required a substitution, surprisingly!). However these solutions aren't like mark schemes, so you're probably right.
I think an actual question will be phrased as
"Solve the differential equation to show "
5. (Original post by ODES_PDES)
I think an actual question will be phrased as
"Solve the differential equation to show "
I second that as a question writer ...
6. (Original post by gagafacea1)
This question is from M5, however it can be relevant to other modules and exam boards, hence the M4+ in the title.

So when I saw part (b), my laziness immediately made me think of just differentiating the given and showing that is equal to , by substituting of course. That way I don't have to do that semi-messy integral that I'll probably get from the differential equation in part (a).

However, knowing the stupidity of some mark schemes, I'm a bit wary of using this in an actual exam. What do you think?
The Edexcel exam questions generally ask you to obtain the differential equation as a "show that" and then don't tell you what the relationship between the variables is, so you don't have the option of differentiating instead of integrating.

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