Solving y' = (y+9x)^2: Methods & Solutions

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The discussion focuses on solving the differential equation y' = (y + 9x)^2. A key method proposed is to use the substitution u = y + 9x, which simplifies the equation into a separable form. This transformation allows for easier integration and solution of the differential equation. Participants emphasize the importance of recognizing substitution techniques in solving nonlinear differential equations.

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gikiian
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1. The problem statement:

y' = (y+9x)^2The attempt at a solution

I just need to know how do you bring it into the separable form. Tell me numerically or just in words, I won't mind.
Which method do I need to use?

Thanks :smile:
 
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Change the dependent variable y to u with the substitution u = y + 9x.
 

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