Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 13.1, Problem 19E
To determine
To classify: The partial
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What is the differential equation of the orthogonal
trajectories of the family of curves
x²-3xy - 2y²=C?
A
B
C
D
(2x - 3y) dx - (3x+4y) dy = 0
(3x+4y) dx + (2x - 3y) dy
= 0
(3x+4y) dx - (2x − 3y) dy = 0
(2x - 3y) dx + (3x+4y) dy = 0
How do I get the P.I xp from the C.F xc on nonhomogeneous 2nd order derivtive equation in this problem. Work on the photos.
What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy- 2y² = C ?
(A
(2x- 3y)dx + (3x+ 4y)dy = 0
B
(3x + 4y) dx – (2x – 3y) dy = 0
(3x + 4y) dx + (2x– 3y) dy = 0
(D
(2x- 3y)dx – (3x+ 4y)dy = 0
Chapter 13 Solutions
Advanced Engineering Mathematics
Ch. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10E
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Prob. 16ECh. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Prob. 30ECh. 13.1 - Prob. 31ECh. 13.1 - Prob. 32ECh. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.4 - Prob. 1ECh. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13.4 - Prob. 8ECh. 13.4 - Prob. 9ECh. 13.4 - Prob. 10ECh. 13.4 - Prob. 11ECh. 13.4 - Prob. 12ECh. 13.4 - Prob. 13ECh. 13.4 - Prob. 15ECh. 13.4 - Prob. 16ECh. 13.4 - Prob. 17ECh. 13.4 - Prob. 18ECh. 13.4 - Prob. 23ECh. 13.5 - Prob. 1ECh. 13.5 - Prob. 2ECh. 13.5 - Prob. 3ECh. 13.5 - Prob. 4ECh. 13.5 - Prob. 5ECh. 13.5 - Prob. 6ECh. 13.5 - Prob. 7ECh. 13.5 - Prob. 8ECh. 13.5 - Prob. 9ECh. 13.5 - Prob. 10ECh. 13.5 - Prob. 11ECh. 13.5 - Prob. 12ECh. 13.5 - Prob. 13ECh. 13.5 - Prob. 14ECh. 13.5 - Prob. 15ECh. 13.5 - Prob. 16ECh. 13.5 - Prob. 17ECh. 13.5 - Prob. 22ECh. 13.6 - Prob. 1ECh. 13.6 - Prob. 2ECh. 13.6 - Prob. 5ECh. 13.6 - Prob. 6ECh. 13.6 - Prob. 7ECh. 13.6 - Prob. 8ECh. 13.6 - Prob. 9ECh. 13.6 - Prob. 10ECh. 13.6 - Prob. 11ECh. 13.6 - Prob. 12ECh. 13.6 - Prob. 13ECh. 13.6 - Prob. 14ECh. 13.6 - Prob. 15ECh. 13.6 - Prob. 16ECh. 13.6 - Prob. 17ECh. 13.6 - Prob. 18ECh. 13.6 - Prob. 19ECh. 13.6 - Prob. 20ECh. 13.7 - Prob. 1ECh. 13.7 - Prob. 2ECh. 13.7 - Prob. 3ECh. 13.7 - Prob. 4ECh. 13.7 - Prob. 5ECh. 13.7 - Prob. 7ECh. 13.7 - Prob. 8ECh. 13.7 - Prob. 9ECh. 13.8 - Prob. 1ECh. 13.8 - Prob. 2ECh. 13.8 - Prob. 3ECh. 13.8 - Prob. 4ECh. 13 - Prob. 1CRCh. 13 - Prob. 3CRCh. 13 - Prob. 4CRCh. 13 - Prob. 5CRCh. 13 - Prob. 6CRCh. 13 - Prob. 7CRCh. 13 - Prob. 8CRCh. 13 - Prob. 9CRCh. 13 - Prob. 10CRCh. 13 - Prob. 11CRCh. 13 - Prob. 12CRCh. 13 - Prob. 13CRCh. 13 - Prob. 14CRCh. 13 - Prob. 15CRCh. 13 - Prob. 16CRCh. 13 - Prob. 17CRCh. 13 - Prob. 18CRCh. 13 - Prob. 19CRCh. 13 - Prob. 20CR
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- 3.Find the differential equations for each familyof curves under the following conditions: a)Straight lines with algebraic sum of the intercepts fixed at k. b)Circles with center on the y –axis. c)Straight lines with slope and y –intercept equal.arrow_forward(8) Find dz if the equation yz – In z = x² +y² defines z as a function of two independent variables r and and partial derivative exists.arrow_forward6. A special class of first-order linear equations have the form a(t)y' (t) + a' (t)y(t) = f(t), where a and f are given functions of t. Notice that the left side of this equation d can be written as the derivative of a product, so the equation has the format(at)y(t)) = a(t)y' (t) + a' (t)y(t) = f(t). Therefore, the equation can be solved by integrating both sides with respect to t. Use this idea to solve the following. ty' (t) +y = 3+t, y(1) = 6 y(t) = where t > 0arrow_forward
- The complementary function(C.F.) of the differential equation(D – 3)°y = cos 3x is O (ci + czx + C3 a)e -3x O (C1 + c2x – C3x²)e3 O (c1 + c2x + c3x²)e3z O (cı + c2x – czx?). The orthogonal trajectories of the family of curves r = f(0) is solve by using the following substitution do = p2 dr dr do dr do do dr dr do do dr dr de do drarrow_forwardIf y is a function of t and z= 4y2 + y' when y=2 find dz/ dt and dy/ dt = - 1- | O 16 17 -17 -8arrow_forwardThe formation of the partial differential equation by eliminating arbitrary function of z = 3f(x³ – y³) is - az dz +x². 3 ду dz dz + x ду dz dz ду az az + x?. dY y² 0 = || ||arrow_forward
- 5. Find the first partial derivatives of w=In(x+2y+3z)arrow_forwardGiven an IVP d"y + an-1(x) dn-ly dy +...+ a1 (x) dx + ao (x)y = g(x) drr-1 у (хо) — Уо, у (tо) — Ул, -.., у" "(2о) — Ул-1 If the coefficients an (x), ..., ao (x) and the right hand side of the equation g(x) are continuous on an interval I and if an (x) +0 on I then the IVP has a unique solution for the point xo e I that exists on the whole interval I. Consider the IVP on the whole real line d'y - 36) dx4 dy + y= sin(x) 1 (x² dz3 x2 + 36 dx у(3) — 916, у (3) — 14, у"(3) — 8, у" (3) — 8, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the intervalarrow_forward1) lim,2 1+t?dt =? x+2 x2-4arrow_forward
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