Solving Differential Equation: dy/dx = e^x + y

wezzo62
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Find the general solution to:
dy/dx = ex+y

Im not sure if I am doing this right or not. i tried saying ex+y = ex x ey and using partial differentiation to solve it but keep getting the same as the question: ex+y
i know differentiating ex gives ex so is it the same in this case?
 
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Why should you use partial differentiation??

You are given a separable differential equation,
\frac{dy}{dx}=e^{x}*e^{y}, or:
e^{-y}dy=e^{x}dx
Thus, you have, by integration:
-e^{-y}=e^{x}+C, where C is a constant of integration.
We now rewrite this as:
e^{-y}=B-e^{x},B=-C
Taking the natural logarithm at both sides yields:
-y=\ln(B-e^{x})
That is:
y(x)=-\ln(B-e^{x})
 
welcome to pf!

hi wezzo62! welcome to pf! :smile:
wezzo62 said:
… i tried saying ex+y = ex + ey

no, ex+y = ex times ey :wink:

try again! :smile:
 


tiny-tim said:
hi wezzo62! welcome to pf! :smile:


no, ex+y = ex times ey :wink:

try again! :smile:

typo, i meant and was writing time not plus
 
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