Find the equation of the solution to dydx=x6y through the point (x,y)=(1,3).
1 answer:
Separate the x's and y's.
dy/y = x^7 dx
Integrate both sides.
ln(abs(y)) = (x^8)/8 + C
To cancel the natural root, make both sides the power to e.
e^ln(abs(y)) = e^((x^8)/8 + C)
abs(y) = e^C * e^((x^8)/8)
y = + or - [e^C * e^((x^8)/8)
Now just bundle the + or - e^C into a single constant. We will call it A.
y = Ae^((x^8)/8)
Now plug in the point (1,3).
3 = Ae^((1^8)/8)
3 = Ae^(1/8)
A = 3/(e^(1/8))
So the equation is:
y = (3/(e^(1/8))*(e^((x^8)/8)
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