You are invited to build differential equations given some starting expressions (picked so that each DE requires a different method for solution.) Good consolidation for students who have already encountered simple DEs.
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This looks like a very interesting and stimulating activity suited to quite able and/or confident students to stretch and challenge them, as the mathematics is quite demanding. I'm quite tempted to try it out on my next Further Maths class and see how it goes. Beware that the given solution to q1 is slightly wrong as the author hasn't turned the coefficient into a power on the LHS when cancelling the logs in the final step.
This is a really nice rich activity for students to consolidate their understanding of differential equations. Students are asked to solve various differential equations of their own construction, each one requires a different method and so this activity will give you a good indication of students understanding. This could be done as an extended plenary, or to get the most out of it you could make this a whole lesson. Thank you for sharing.
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