Advise is needed for find derivative for Taylor series: dy/dx = 3 - 2xy

[PA3040D]

Dear experts , I have attempted to solve a portion of the following question. However, I am unsure about the correctness of the derivatives I have calculated. Additionally, as the question lacks initial conditions , I would appreciate any advice or guidance you can provide.

Question



My Start

 

[PA3040D]

Problem is solved

I got initial condition as y(0)=1

 

[PA3040D]

Dear Expert,

Although my initial problem has been resolved, I need further clarification on how to determine when a question requires implicit differentiation, as I did in my first post. Could you please advise?

 

[mario99]

When you differentiate a variable ([imath]y[/imath]) with respect to another variable ([imath]x[/imath]), but the first variable ([imath]y[/imath]) is not the subject (not isolated), you use implicit differentiation.

For example:

[imath]y = 4x^2[/imath]

Here [imath]y[/imath] is the subject, means it is isolated alone. In this case you differentiate normally.

Another example:

[imath]y^2 = 4x^2y[/imath]

Here [imath]y[/imath] is not the subject, means it is not isolated alone. In this case you use implicit differentiation.