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

[wezzo62]

Find the general solution to:
dy/dx = e^x+y

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

 

[arildno]

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:
$$y(x)=-\ln(B-e^{x})$$

 

[tiny-tim]

welcome to pf!

hi wezzo62! welcome to pf!

… i tried saying e^x+y = e^x + e^y

no, e^x+y = e^x times e^y

try again! ​

 

[wezzo62]

hi wezzo62! welcome to pf!


no, e^x+y = e^x times e^y

try again! ​

typo, i meant and was writing time not plus