If x(t) is a solution to the equation x' = f(x), show that x(t + c) is also a solution, for any constant c. is x(t) + c a solution? explain why.

Yes, x(t)+C is also a solution of given equation.

Step-by-step explanation:

We are given that x(t)  is a solution of the equation x'=f(x)

We have to show that x(t+c) is also a solution of given equation and check x(t)+c is a solution of equation.

Suppose x'=1

Integrating on both sides

Then , we get

Where C is integration constant.

Now, t replace by  t+c

Then, we get

because c+C=K

Different w.r.t then we get

Therefore, x(t+c) is also solution because it satisfied the given equation.

Now, x(t)+C=t+(c+C)=t+L where L=c+C=Constant

Differentiate w.r.t time

Then, we get

Yes, x(t)+C is also solution of given equation because it satisfied given equation

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d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.