Write out the first 4 terms of y1 and y2: ( x+2 ) y" - 3y'...

Write out the first 4 terms of y1 and y2:

( x+2 ) y" - 3y' + 2xy = 0 ; x0 = 3

Expert Solution

Colby Messinger answered 2 years ago

The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t...

The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t where 0 ≤ t ≤ 1 describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). Use a graphing device to draw the triangle with vertices A(1, 1), B(4, 3), C(1, 6). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.)

Let x,y ∈ R3 such that x = (x1,x2,x3) and y = (y1,y2,y3) determine if <x,y>=...

Let x,y ∈ R3 such that x = (x1,x2,x3) and y = (y1,y2,y3) determine if <x,y>= x1y1+2x2y2+3x3y3 is an inner product

a) The functions y1 = x^2 and y2 = x^5 are two solutions of the equation...

a) The functions y1 = x^2 and y2 = x^5 are two solutions of the equation x^2 y ″ − 6 x y ′ + 10 y = 0. Let y be the solution of the equation x^2 y ″ − 6 x y ′ + 10 y = 3 x^5 satisfyng the conditions y ( 1 ) = 0 and y ′ ( 1 ) = 1. Find the value of the function f ( x ) = y ( x )...

Two waves y1(x,t) and y2(x,t) propagate in the air: y1 = A sin(6x - 12t) y2...

Two waves y1(x,t) and y2(x,t) propagate in the air: y1 = A sin(6x - 12t) y2 = A sin(5x - 10t) Find: a) The equation of the resulting pulse, y1 + y2. b) The distance between 2 consecutive zeros in the elongation. c) The distance between 2 consecutive absolute maxima of the elongation.

y1 = -109.7ln(x)+336.56 y2 = -126.9ln(x)+395.81 where y1 = storage time in days for sprouting y2...

y1 = -109.7ln(x)+336.56 y2 = -126.9ln(x)+395.81 where y1 = storage time in days for sprouting y2 = storage time in days for spoilage x = storage temperature in oC a. How many days are potatoes expected to spoil if stored at 18oC? b. A farmer discovered his stored potatoes showing a sign of wrinkles and dark spot after 15 days. Determine at what temperatures they must has been stored to cause the spoilage. c. A food processing company wants to...

Maximize p = x subject to x − y ≤ 4 −x + 3y ≤ 4...

Maximize p = x subject to x − y ≤ 4 −x + 3y ≤ 4 x ≥ 0, y ≥ 0. HINT [See Examples 1 and 2.] p = (x, y) = ____________

The joint density of Y1, Y2 is given by f(y) = k, −1 ≤ y1 ≤...

The joint density of Y1, Y2 is given by f(y) = k, −1 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1, y1 + y2 ≤ 1, y1 − y2 ≥ −1, 0, otherwise a. Find the value of k that makes this a probability density function. b. Find the probabilities P(Y2 ≤ 1/2) and P(Y1 ≥ −1/2, Y2 ≤ 1/2 c. Find the marginal distributions of Y1 and of Y2. d. Determine if Y1 and Y2 are independent e....

We define a relation ∼ on R^2 by (x1,y1)∼(x2,y2) if and only if (y2−y1) ∈ 2Z....

We define a relation ∼ on R^2 by (x1,y1)∼(x2,y2) if and only if (y2−y1) ∈ 2Z. Show that the relation∼is an equivalence relation and describe the equivalence class of the point (0,1).

(1 point) In general for a non-homogeneous problem y′′+p(x)y′+q(x)y=f(x) assume that y1,y2 is a fundamental set...

(1 point) In general for a non-homogeneous problem y′′+p(x)y′+q(x)y=f(x) assume that y1,y2 is a fundamental set of solutions for the homogeneous problem y′′+p(x)y′+q(x)y=0. Then the formula for the particular solution using the method of variation of parameters is yp=y1u1+y2u2 where u′1=−y2(x)f(x)W(x) and u′2=y1(x)f(x)W(x) where W(x) is the Wronskian given by the determinant W(x)=∣∣∣y1(x)y′1(x)y2(x)y′2(x)∣∣∣ So we have u1=∫−y2(x)f(x)W(x)dx and u2=∫y1(x)f(x)W(x)dx. NOTE When evaluating these indefinite integrals we take the arbitrary constant of integration to be zero. In other words we have...

Sketch the region enclosed by the given curves and find its area. a) y=4/x,y=4x,y=(1/4)x,x>0 b) x=y2−4y,x=2y−y2

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