What is a solution to the differential equation $dy/dx=4y$ ?

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Answer 1 · 2016-08-02T03:13:42

$y=Ce^(4x)$

We can separate the variables:

$dy/dx=4y" "=>" "dy/(4y)=dx$

Integrate both sides:

$intdy/(4y)=intdx" "=>" "1/4intdy/y=intdx" "=>" "1/4ln(y)=x+C$

Solving for $y$ :

$ln(y)=4x+C" "=>" "y=e^(4x+C)=e^(4x)*e^C=Ce^(4x)$

What is a solution to the differential equation dy/dx=4ydy/dx=4y?