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
A) A person who buys items in the store
A consumer is someone who takes , or in this case buys. I hope I helped!
Answer:
y-5=1/4(x-3)
Step-by-step explanation:
first you need to find the slope.
5-7 over 3-6 = -1/-4 or 1/4
next put into point-slope form.
y-y1=m(x-x1)
or y-5=1/4(x-3)
The answer should be b. because 4(4) = 16 and that’s closer to 18.4 than the others.
It is given thatΔ QRS ≅Δ TUV
Out of all the given options
(C) QS= TV [C P C T}
(D) QR =TU
(E) S = V
(F) R= U
C, D,E, F are correct options.
Because when two triangles are congruent their corresponding parts are equal.
CPCT means corresponding parts of congruent triangles.
All these options are congruent by CPCT.
Side QR is congruent to TU.
Side Q S is congruent to TV.
Angle S is Congruent to Angle V.
Angle R is congruent to Angle U.
The meaning of congruency of shapes is that the two or many more shapes are identical.
