Differential Equations:Eliminate the arbitrary constants: y = e2* (C1 cos x + c, sin x)а. у" — 4y + 5у%3D0b. y" + 4y' - 5у %3D0с. у" + 4y' + 5у %3D0d. y" — 4y' — 5у %3D0|||

In this question , we can eliminate the arbitrary constant by differentiate the given equation.

Answered: Differential Equations: Eliminate the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Which of the following is the Euler differential equation whose general solution is y = c,x² + ? а. x?у" + 2ху' — бу %3D0 | b. x?у" — 2ху' + бу %3D0 с. х"у" - 2ху' бу %3D 0 d. x²y" + 2xy' + 6y = 0 e. x²y" + xy' + 2y = 0
3t --- 3t a. Verify that y(t) = b. Verify that yo(t) = = is a solution to y '(t) substituting it into the differential equation. (Enter the terms in the order given.) y' (t) = 5t + 1 2t 4t + 2 = Use angle brackets, ( and ), to indicate vectors, and separate the components with commas. E.g. (e', t², 2e²¹). = 1 -2 2 -2 2 1 2 2 1 1 [ -2 is a particular solution to -2 21 1 2 1 2 y(t) + 2 y(t) by [1 4- (4t+ 4+ 5t) 0 2 (14t+2+ 4t) by substituting it into the differential equation. (Enter the terms in the order given.) Use angle brackets, ( and ), to indicate vectors, and separate the components with commas. E.g. (3, 3t², 2t + 1).
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Which of the following is the general solution to the differential equation dx := 2 (3x + y)² – 1 ? y2 = C(x + 1) Arctan (3x — у) — 2х2 — С %3D O D A Arcsin (3x — у) — 2х %3D С Arctan (3x + у) — 2х %3D С В
Which of the following equations is NOT a variable separable differential equation? " ydy - (e-" + e -²₁-x) dx = B (x²-x²) dx + (y² + xy²) dy = 0 A D sec y dy dx 0 + sin (x-y) = sin(x + y) (xy - x²) dy - y² dx = 0
What is of the differential equation 2z (32 +y - ye) dz + (z² + 3y² + e * dr + (2 + 3y + e ) dy = 0 ? O 22 4ze O 2z 6yc O2r 2re 2 O.2x

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Differential Equations: Eliminate the arbitrary constants: y = e2* (c, cos x + c2 sin x) а. у" — 4y' + 5у —D0 b. y" + 4y' - 5у %3D0 с. у" + 4y' + 5у %3D0 d. y" — 4y' — 5у — 0