Answer:
y=2-e^(1-x)
Step-by-step explanation:
This can be solved by separating the variables.
dy/dx=2-y
Multiply both sides by dx
Divide 2-y on both sides
dy/(2-y)=dx
Integrate both sides
-ln|2-y|=x+c
Multiply both sides by -1
ln|2-y|=-x-c
Equivalent logarithm form
2-y=e^(-x-c)
Minus 2 on both sides
-y=e^(-x-c)-2
Multiply both sides by -1
y=-e^(-x-c)+2
The ordered pair (1,1) belongs to the curve so we have
(I'm going to use this earlier form -ln|2-y|=x+c)
-ln|2-1|=1+c
-ln|1|=1+c
-0=1+c
0=1+c
Minus 1 on both sides
-1=c
Answer:
y=-e^(-x-(-1))+2
Or
y=-e^(-x+1)+2
Or
y=2-e^(1-x)
