, 24.01.2020howme

# In each of problems 5 through 10, verify that each given function is a solution of the differential equation. y''-y=0, y1(t)=e^t , y2(t)=cosht markeishamarsh4
Hope this helps you.  Niah628

x⁻²

Step-by-step explanation:

If y = e²ˣ, y' = 2e²ˣ.

2xe²ˣ + 2e²ˣ ≠ 0

If y = x², y' = 2x.

2x² + 2x² ≠ 0

If y = x⁻², y' = -2x⁻³.

-2x⁻² + 2x⁻² = 0 Svetakotok

Since L.H.S = R.H.S = 0, for both and , y₁ and y₂ both satisfy the equation y" - y = 0 and are thus solutions to the differential equation.

Step-by-step explanation:

To check whether the given functions are solutions the given differential equation, we differentiate the functions and then insert it into the given equation.

So y" - y = 0 and Substituting these values of y and y" into the left hand side of the equation, we have

y" - y Since L.H.S = R.H.S

So is a solution of the differential equation.

When Substituting y and y" into the left hand side of the equation, we have

y" - y Since L.H.S = R.H.S

So, is a solution of the differential equation. 1Angel2Got3Brains

For First Solution:  is the solution of equation y''-y=0.

For 2nd Solution:  is the solution of equation y''-y=0.

Step-by-step explanation:

For First Solution: In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives. First order derivative: 2nd order Derivative: Put Them in equation y''-y=0

e^t-e^t=0

0=0

Hence is the solution of equation y''-y=0.

For 2nd Solution: In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives. First order derivative: 2nd order Derivative: Put Them in equation y''-y=0

cosht-cosht=0

0=0

Hence is the solution of equation y''-y=0.  ### Other questions on the subject: Mathematics Mathematics, 21.06.2019, gghkooo1987 Mathematics, 21.06.2019, cykopath Mathematics, 21.06.2019, lilbit217
first, we will find the distance between airport and origin then we will double it and we'll get the distance between airport and warehouse.by Pythagoras theorem :-let base be = 42...Read More Mathematics, 21.06.2019, xxaurorabluexx
The volume is Step-by-step explanation:* Lets talk about the shell method- The shell method is to finding the volume by decomposing  a solid of revolution into cylindrical shells-...Read More Mathematics, 21.06.2019, odellbeckham7171   