Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 11.1, Problem 25E
To determine
The solution of the non-linear plane autonomous system by changing to polar coordinates and its geometric behavior
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9. Form the differential equation of the three-parameter family of conics y = ae* + be2x + ce¬3x
where a, b and c are arbitrary constants.
2. Which of the following is a general solution to the following:
x²y" + xy' + (36x² - 1) y
(Hint: As discussed in the lecture, use Y, only when J, and J-, are linearly dependent).
A. y = c₁J₁(2x) + C₂J_1(2x)
6
B. y = C₁J₁(x) + C₂Y₁(x)
3
3
C. y = c₁₂/₁(6x) + C₂Y₁(6x)
0
D. y = c₁J₁(6x) + c₂] _1(6x)
2
Question 1
Which of the following is a nonhomogeneous linear dif ferential equation with constant coefficients?
A
(x²D³– D²– xD)y=6x+ 5cosx
B) none of the given choices
(x- 1)y"- xy'+y=0
5y" - бу" + у30
D³(D²- 4)y=3x+2e -3x
Chapter 11 Solutions
Advanced Engineering Mathematics
Ch. 11.1 - Prob. 1ECh. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11 - Prob. 1CRCh. 11 - Prob. 2CRCh. 11 - Prob. 3CRCh. 11 - Prob. 4CRCh. 11 - Prob. 5CRCh. 11 - Prob. 6CRCh. 11 - Prob. 7CRCh. 11 - Prob. 8CRCh. 11 - Prob. 11CRCh. 11 - Prob. 12CRCh. 11 - Prob. 13CRCh. 11 - Prob. 15CRCh. 11 - Prob. 16CRCh. 11 - Prob. 17CR
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- Example 11.1. Classify the following equations : a²u 22u d²u du du +4. +4 J + 2- = 0 Əxdy oy² ax dy a²u •+ (1 - y²¹). = 0, -∞ < x ∞, -1arrow_forward1-2x Question 7 What is the x-intercept of the following equation: y= 1/2x+1 A) (-2,0) B. None of the these (-2,1) (0,2) E) (2,0) F (0,-2) Question 8 Create the equation of a ine tinat is oerpendicular to 2x-y=4 andarrow_forwardMatch each linear system with one of the phase plane direction fields. (The blue lines are the arrow shafts, and the black dots are the arrow tips.) ? ✓ | 1. z ' = || a' ? 2. ': = ? 3.' = 4. a: = 11 8] -10 3 1 5 -2 1 -5 -13 10] -10 x2 A x2 с x1 (x2 B 2x2/ D Note: To solve this problem, you only need to compute eigenvalues. In fact, it is enough to just compute whether the eigenvalues are real or complex and positive or negative.arrow_forward15 Give the properties for the equation 3y 2 - 2y + x + 1 = 0. Center (-1, 1/3) (-2/3, 1/3) (-8/9, 1/3)arrow_forward13. The standard form of 3dy-xydx = 3y3e4x/3 by Bernoulli's equation is:arrow_forward4. Obtain the differential equation of the family of lines passing through the center of the conics described by the equation x2 + 4y² + 2x – 8y +1 = 0. -arrow_forwardThis is the fourth part of a four-part problem. If the given solutions ÿ₁ (t) = - [²2²], 2(0)-[¹7¹]. form a fundamental set (i.e., linearly independent set) of solutions for the initial value problem 21-² -21-2 y' = - [22 12t¹+2t 27 2t ¹-2t 2 [²], 2t | Ü‚ ÿ(5) — [34], t = t> 0, impose the given initial condition and find the unique solution to the initial value problem for t> 0. If the given solutions do not form a fundamental set, enter NONE in all of the answer blanks y(t) = (arrow_forwardProblem 5. Find and Classify the critical point of (x,y)=192x³+y²–4xy² on the triangle with vertices (0,0), (4,2) and (-2,2).arrow_forwardty'''+2y''+y'+ty=0 What is the Wronskian of linearly independent solutions?arrow_forwardProblem 2. Consider the equation: x?y"(x) – xy' +y = 0. Given that yı(x) = x is a solution of this equation. Use the method of reduction of order, find the second solution y2(x) of the equation so that y1 and y2 are linearly independent. (Hint: y2(x) should be given in the form y2(x) = u(x)y1(x). Substitute it into the equation to find u(x).) %3Darrow_forwardQ1: Formulate the equation of plane in space that contain two points (2,4,-1) and (1,3,-2) and perpendicularly intersects with the plane 3x+5y+4z=487. Q2: Solve the following differential equation in two ways. (2xy + x?)dx + (x2 + y²)dy = 0 Q3: Find the shortest line from a point to a plane, justify your answer by calculations. Hint: you can choose any coordinates of the points and equation of the plane. Q4: Design the biggest box (volume) without cover that made from 6m2 of aluminum. Hint: Use Lagrange Multipliers Methodarrow_forward2. A bug is crawling along the surface defined by x³ + y²z – z³ = 5. The bug is currently at the point (2, –2, –1). (a) If the bug moves along the surface by increasing its y-coordinate and keeping x = quickly is its z-coordinate changing? = 2, then how (b) If, instead, the bug moved from (2, –2, –1) along the surface by increasing its z-coordinate, and keeping y = -2, then how quickly is its x-coordinate changing?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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