How to solve (x+1)dx + e^y dy = 0 at points (0,1)

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Answer 1

solve (x+1)dx + e^y dy = 0 at points (0,1)

 

Separate variables:

 

(x+1)dx = - e^y dy

 

∫(x+1)dx = - ∫ e^y dy

 

x^2/2 + x = - e^y + C

 

at (0,1): 0 + 0 = -e + C

 

C = e