Proving the equation is a solution to differential equation

dexby

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I've been stuck on this question, since yesterday night. My troubles occur when most of the pronumerals are constants. My method is to differentiate the equation, and to turn it relate it to the differential equation. I will provide the original equation I am having trouble on, and then a simpler form of the same type of question, completed by the textbook. Help will be appreciated :)phpiynCY2.png
 

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I've been stuck on this question, since yesterday night. My troubles occur when most of the pronumerals are constants. My method is to differentiate the equation, and to turn it relate it to the differential equation. I will provide the original equation I am having trouble on, and then a simpler form of the same type of question, completed by the textbook. Help will be appreciated :)View attachment 33351
Please show your actual work, so we can see if you have made any mistakes in your differentiation, or in your algebra. Presumably your method itself is correct in general, just not some details. Constants should make it easier, not harder (apart from making algebra more complicated).
 
I've been stuck on this question, since yesterday night. My troubles occur when most of the pronumerals are constants. My method is to differentiate the equation, and to turn it relate it to the differential equation. I will provide the original equation I am having trouble on, and then a simpler form of the same type of question, completed by the textbook. Help will be appreciated :)View attachment 33351
If it helps, I simplified the expression for N a little first, dividing everything by [imath]N_0[/imath] and then letting [imath]a=\frac{k}{N_0}-b[/imath]. (This leaves you with fewer balls to juggle, so you're less likely to drop any.) Then I just differentiated, evaluated [imath]kN-bN^2[/imath], and compared the two.
 
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