Answer:
Laplace transforms turn a Differential equation into an algebraic, so we can solve easier.
y'= pY-y(0)
y"=p²Y - py(0)- y'(0)
Substituting these in differential equation :
p²Y -py (0) -y' (0)-6(pY-y(0)) + 13Y
Substituting in the initial conditions given , fact out Y, and get:
Y( p²-6p+13) = -3
Y=-3/ p²-6p+13
now looking this up in a table to Laplace transformation we get:
y=-3/2.e³т sin(2t)
for the last one, find the Laplace of t∧2 . which is 2/p³
pY - y(0)+ 5Y= 2/p³
Y= 2/p³(p+5)
Taking partial fractions:
Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³
Learn more about differential equation here:
brainly.com/question/14620493
#SPJ4
#1. 1000
#2. 1/45 (decimal is .02 with the line above the two
#3. 32/9
#4. 1/20 (decimal form .05
#5. 4
#6. 47/4 (decimal is 11.75)
#7. 1/4 (decimal 0.25
#8. 1/2 decimal is 0.5
#9. 45
#10. 12
I really hope this help
B.28 square inches
This can be a face because it is equal to 4*7
I think the answer is irrational numbers, but i'm not sure
The equation that represents the line that is perpendicular is
3y + 5x = -42
The standard equation of a line in point-slope form is expressed as:
- m is the slope of the lne
- (x1, y1) is any point on the line.
- Given the equation y = 3/2x + 1, the slope of the line is 3/5
- The s<u>lope of the line perpendicular</u> is -5/3
Substitute the point (-12, 6) and the slope m = -5/3 into the equation above to have:
Hence the equation that represents the line that is perpendicular is
3y + 5x = -42
Learn more on equation of a line here:brainly.com/question/19417700
