1 Answer

SergVro · Answer 1 · 2024-04-28T01:09:51+0000

The solution to the differential equation y'(x) = y for y(1) = 6 is
$y = 6e^{x-1$

How to solve the differential equation

From the question, we have the following parameters that can be used in our computation:

y'(x) = y

y(1) = 6

This can be expressed as

dy/dx = y

So, we have

dy/y = dx

Integrate both sides

$\int\limits {\frac 1y} \, dy = \int\limits dx$

This gives

ln|y| = x + c

Raise both sides of the expression by 2

y = e^(x + c)

This gives

$y = ce^{x$

Recall that

y(1) = 6

So, we have

6 = ce^(1)

6 = ce

This gives

c = 6/e

So, we have

$y = (6)/(e)e^{x$

$y = 6e^{x-1$

Hence, the solution to the differential equation is
$y = 6e^{x-1$

Question

Solve the differential equation

y'(x) = y

y(1) = 6

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