Solve the equation. \frac{dy}{dx}=7y, and y=1 when z=0.

tricotasu 2021-09-28 Answered
Solve the equation.
dydx=7y, and y=1 when z=0.
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Expert Answer

bahaistag
Answered 2021-09-29 Author has 101 answers
Given,
dydx=7y
dyy=7dx
Now integrating on both sides, we get
dyy=7dx
lny=7x+C1
y=e7x+C1   [lnx=yx=ey]
y=e7xeC1
y=Ce7x (1) where eC1=C
Now given that y = 1 when x = 0, therefore equation (1) becomes,
1=Ce7(0)C=1
Now put C=1 in equation (1), we get
y=1e7x
y=e7x
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