find the general solution to this differential equation?

Question

y'= y e^x + e^x

Answer 1

y'= y e^x + e^x
y'= e^x (y+1)

y'/(y+1)=e^x
dy/(y+1)=e^xdx

lny=e^x+C

y=e^(e^x+C)

Answer 2

are u trying to find the derivitive?
if so this is how u do it

first u take the derivitive of the equation
(ye^x)'+(e^x)' the sum rule
use product rule and chain rule to get (ye^x)'=y'e^x+ye^x
y'e^x+ye^x+(e^x)
get y' on one side y'=(-ye^x-(e^x))/e^x
simplafy y'=-1-y
answer y'=-1-y

Answer 3

okey dokey!
did you have an initial condition?
This is a separable DEQ
y ' = e^x( y + 1)
1/(y+1) dy = e^x dx
ln I y+1 I = e^x + C
y+1 = e^ (e^x + C) =same as e^(e^x)e^C = A*e^(e^x)

y = A * e^(e^x) - 1

=)


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Answer 4

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