Answer:
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
![y_{1} (t) = e^{t}\\y_{1}' (t) = e^{t}\\ y_{1}" (t) = e^{t}](https://tex.z-dn.net/?f=y_%7B1%7D%20%28t%29%20%3D%20e%5E%7Bt%7D%5C%5Cy_%7B1%7D%27%20%28t%29%20%3D%20e%5E%7Bt%7D%5C%5C%20y_%7B1%7D%22%20%28t%29%20%3D%20e%5E%7Bt%7D)
Substituting these values of y and y" into the left hand side of the equation, we have
y" - y
![y_{1}" (t) - y_{1} (t) = e^{t} - e^{t} = 0](https://tex.z-dn.net/?f=y_%7B1%7D%22%20%28t%29%20-%20y_%7B1%7D%20%28t%29%20%3D%20e%5E%7Bt%7D%20-%20e%5E%7Bt%7D%20%3D%200)
Since L.H.S = R.H.S
So
is a solution of the differential equation.
When
![y_{2} (t) = cosh(t)\\ y_{2}'(t) = sinh(t) \\y_{2}"(t) = cosh(t)](https://tex.z-dn.net/?f=y_%7B2%7D%20%28t%29%20%3D%20cosh%28t%29%5C%5C%20y_%7B2%7D%27%28t%29%20%3D%20sinh%28t%29%20%5C%5Cy_%7B2%7D%22%28t%29%20%3D%20cosh%28t%29)
Substituting y and y" into the left hand side of the equation, we have
y" - y
![y_{2}"(t) - y_{2} (t) = cosh(t) - cosh(t) = 0](https://tex.z-dn.net/?f=y_%7B2%7D%22%28t%29%20-%20y_%7B2%7D%20%28t%29%20%3D%20cosh%28t%29%20-%20cosh%28t%29%20%3D%200)
Since L.H.S = R.H.S
So,
is a solution of the differential equation.
Answer:
C
Step-by-step explanation:
if you multiply 2.3 times pi you get the answer
Lets factor 8x^2 - 10x - 25
= 8x^2 -20x + 10x - 25
= 4x(2x - 5) + 5(2x - 5) 2x-5 is common to both parts so factors are:-
= (4x + 5)(2x - 5)
So its C
Answer:
12 measures
Step-by-step explanation:
Step 1:
64 : 8 Ratio
Step 2:
64 : 8 = 96 : x Equation
Step 3:
64x = 768 Multiply
Step 4:
x = 768 ÷ 64 Divide
Answer:
x = 12
Hope This Helps :)