In this problem you will solve the non-homogeneous differential equationon the interval -π/6 < x < π/6.(1) Let C₁ and C₂ be arbitrary constants. The general solution of the related homogeneous differential equation y' +9y = 0 is the functionYh(x) = C₁ y₁ (x) + C₂ Y2(x) = C₁+C₂(2) The particular solution y(x) to the differential equation y" +9y = sec²(3x) is of the form yp(x) = y₁(x) u₁(x) + y2(x) u2(x)where u₁(x) =and u₂(x)(3) It follows thatu1(r)thus yp(x):=y"' +9y = sec² (3x)=and u₂(x) =(4) Therefore, on the interval (-π/6, π/6), the most general solution of the non-homogeneous differential equation y" +9y = = sec² (3x)is y = C₁+C₂+

Answered: In this problem you will solve the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The differential equation 3Y = y – y? has one of the following one parameter families as its general solution 1 1+ ce-* 1 y = c+ x? Find the solution such that y(0) = 2:
The indicated function y₁(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, e-/P(x) dx V₂ = V₁(x) [² Y₂ = y} (x) dx (5) as instructed, to find a second solution y₂(x). (1 - 2x - x²)y" + 2(1+x)y' - 2y = 0; y₁ = x + 1
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SOLVE STEP BY STEP IN DIGITAL FORMAT 2. The solution of the differential equation 4 0x² a) U(x, y) = sen(x - 2y) b) U (x, y) = 8²U dy² 0 (2x - y²) c) U(x, y) = (x2² - 2y)
Let r(t)=cos 2t i +sin 2t j + t k be a vector function. Which of the followings are true for this function? I. Tangent vector is constant at any point. II. Length of tangent vector at any point is constant. II. Tangent vector is (0,2,1) at the point (1,0,0). IV. Curvature at a point (a, b, 4а+b c) is 50 V. Arclength of the curve from a point (a, b, c) to a point (d, e, f) is given by V5dt O a. II, II, IV Ob. II, II, V O C. I, II, V Od.I, II, IV
The general solution to the differential equation y"+e²x-6)y=0 has the form 2x-6)y=0 y=C₁ Ja (f(x)) + C₂ Ya (f(x)). Find the value of a and the function f(x). and a = f(x) = Hint: Try using a new independent variable z=ex.
Determine the form of a particular solution y,(x) for the differential equations (a) y" + 6y/ + 13y = e# cos(2a) (b) y" + 3y/ + 2y = r(e - e-2") (c) y" + 4y = 3r cos(2r) -3r using the method of undetermined coefficients (Do not solve the equation).

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