Answer:
The solution to the Euler equation
t²y'' + 5ty' + 3y = 0
is
y = C1/t + C2/t³
Step-by-step explanation:
We are required to solve the Euler equation
t²y'' + 5ty' + 3y = 0...........................(1)
Let x = lnt............................................(2)
=> t = e^x
Let d/dx be D
dy/dt = dy/dx × dx/dt
= (1/t)dy/dx
=> tdy/dt = dy/dx = Dy.....................(3)
Again, d²y/dt² = d/dt (dy/dt) = d/dt[(1/t)dy/dx] = (-1/t²)dy/dx + (1/t)d²y/dx² × dx/dt
= (-1/t²)(d²y/dx² - dy/dx) = (1/t²)(D² - D)
t²d²y/dt² = D(D - 1)y .........................(4)
Using (3) and (4) in (1)
t²y'' + 5ty' + 3y = D(D - 1)y + 5Dy + 3y = 0
(D² - D + 5D + 3)y = 0
(D² + 4D + 3)y = 0
The auxiliary equation is
m² + 4m + 3 = 0
(m + 1)(m + 3) = 0
m = -1, -3
y = C1e^(-x) + C2e^(-3x)
But t = e^x
So,
y = C1/t + C2/t³
Step-by-step explanation:
The Real Answer Is 63
Maybe Positive Or Negative
Answer:
Length of a Road
Step-by-step explanation: No man that has ever lived (Well unless they're a nephilim or smth) is over a mile tall. Swimming pools and buildings aren't usually big enough to be measured in miles unless they're either a skyscraper or a Wisconsin water park attraction.
Answer:
<h2>
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Step-by-step explanation:
5 1/2 , 6 3/4 , 4 2/3
Convert to decimals
5.5 , 6.75 , 4.67
Add
16.92
She worked 16.92 hours
Convert to mixed fraction
<h2>
</h2>
Hope this helps :)
Parallel lines have the same slope. The slope of y = -1/3 x + 4 is -1/3.
The equation is
(y - 5) = -1/3 (x - 6)
y = -1/3 x -1/3 (- 6) + 5 = -1/3 x + 2 + 5 = -1/3 + 7
The equation is: y = - 1/3 x + 7
y = -1/3 x
