Answer:
y = -ln(-e^x + 5)
Step-by-step explanation:
I assume you mean:
dy/dx = e^(y + x)
Use exponent properties:
dy/dx = (e^y) (e^x)
Separate the variables:
e^(-y) dy = e^x dx
Integrate:
-e^(-y) = e^x + C
Solve for y:
e^(-y) = -e^x − C
-y = ln(-e^x − C)
y = -ln(-e^x − C)
Use initial condition to solve for C:
-ln 4 = -ln(-e^0 − C)
4 = -1 − C
C = -5
Therefore, the equation is:
y = -ln(-e^x + 5)
