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

Solve the equation.
$\frac{dy}{dx}=7y$, and y=1 when z=0.
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bahaistag
Given,
$\frac{dy}{dx}=7y$
$⇒\frac{dy}{y}=7dx$
Now integrating on both sides, we get
$\int \frac{dy}{y}=\int 7dx$
$⇒\mathrm{ln}y=7x+{C}_{1}$

$⇒y={e}^{7x}\cdot {e}^{{C}_{1}}$

Now given that y = 1 when x = 0, therefore equation (1) becomes,
$1=C{e}^{7\left(0\right)}⇒C=1$
Now put C=1 in equation (1), we get
$y=1\cdot {e}^{7x}$
$⇒y={e}^{7x}$