Which of the following is a solution to the second order differential equation LaTeX: y''=-4y y ″ = − 4 y ? To answer this quest
ion, attempt to verify each of the following proposed solutions. a. LaTeX: y=\sin2t y = sin 2 t b. LaTeX: y=-\frac{2}{3}t^3 y = − 2 3 t 3 c. LaTeX: y=\cos2t y = cos 2 t d. LaTeX: y=e^{2t} y = e 2 t e. LaTeX: y=\frac{y''}{-4}
1 answer:
Answer:
- y = sin(2t)
- y = cos(2t)
Step-by-step explanation:
In the case of each of the answers listed above, the second derivative is equal to -4 times the function, as required by the differential equation.
For y = 2/3t^3, the second derivative is 4t, not -4y.
For y = e^(2t), the second derivative is 4y, not -4y.
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The graph shows the sum of the second derivative and 4y is zero for the answers indicated above, and not zero for the other two proposed answers.
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The only way to solve if it is equal to something
assuming that the teacher wanted you to make it equal to zero do
0=-3x^2-21x-54
remember if we can do
xy=0 then assume x and y=0
so factor
0=-3x^2-21x-54
undistribute the -3
0=-3(x^2+7x+18)
remember 0 times anything=0 so
x^2+7x+18 must equal zero
use quadratice formula which is
if you have
ax^2+bx+c=0 then
x=
x^2+7x+18
a=1
b=7
c=18
x=
x=
x=
i=√-1
x=
the zerose would be
x=
or 
assuming that the teacher wanted you to make it equal to zero do
0=-3x^2-21x-54
remember if we can do
xy=0 then assume x and y=0
so factor
0=-3x^2-21x-54
undistribute the -3
0=-3(x^2+7x+18)
remember 0 times anything=0 so
x^2+7x+18 must equal zero
use quadratice formula which is
if you have
ax^2+bx+c=0 then
x=
x^2+7x+18
a=1
b=7
c=18
x=
x=
x=
i=√-1
x=
the zerose would be
x=