dy/dx= e^(2x+y)
obtaining an expression for y in terms of x
where y=0 when x=0
obtaining an expression for y in terms of x
where y=0 when x=0
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dy/dx = e^(2x + y)
dy/dx = e^(2x) * e^(y)
dy / e^(y) = e^(2x) * dx
e^(-y) * dy = e^(2x) * dx
Integrate
-e^(-y) = (1/2) * e^(2x) + C
y = 0 when x = 0
-e^(0) = (1/2) * e^(0) + C
-1 = (1/2) * 1 + C
-3/2 = C
-e^(-y) = (1/2) * (e^(2x) - 3)
e^(-y) = (1/2) * (3 - e^(2x))
-y = ln((3 - e^(2x)) / 2)
y = ln(2 / (3 - e^(2x)))
dy/dx = e^(2x) * e^(y)
dy / e^(y) = e^(2x) * dx
e^(-y) * dy = e^(2x) * dx
Integrate
-e^(-y) = (1/2) * e^(2x) + C
y = 0 when x = 0
-e^(0) = (1/2) * e^(0) + C
-1 = (1/2) * 1 + C
-3/2 = C
-e^(-y) = (1/2) * (e^(2x) - 3)
e^(-y) = (1/2) * (3 - e^(2x))
-y = ln((3 - e^(2x)) / 2)
y = ln(2 / (3 - e^(2x)))