Solve the equation.

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

tricotasu
2021-09-28
Answered

Solve the equation.

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

You can still ask an expert for help

bahaistag

Answered 2021-09-29
Author has **101** answers

Given,

$\frac{dy}{dx}=7y$

$\Rightarrow \frac{dy}{y}=7dx$

Now integrating on both sides, we get

$\int \frac{dy}{y}=\int 7dx$

$\Rightarrow \mathrm{ln}y=7x+{C}_{1}$

$\Rightarrow y={e}^{7x+{C}_{1}}\text{}\text{}\text{}[\because \mathrm{ln}x=y\Rightarrow x={e}^{y}]$

$\Rightarrow y={e}^{7x}\cdot {e}^{{C}_{1}}$

$\Rightarrow y=C{e}^{7x}\to \text{}\left(1\right)\text{}where\text{}{e}^{{C}_{1}}=C$

Now given that y = 1 when x = 0, therefore equation (1) becomes,

$1=C{e}^{7\left(0\right)}\Rightarrow C=1$

Now put C=1 in equation (1), we get

$y=1\cdot {e}^{7x}$

$\Rightarrow y={e}^{7x}$

Now integrating on both sides, we get

Now given that y = 1 when x = 0, therefore equation (1) becomes,

Now put C=1 in equation (1), we get

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