3. If M(x, y) is homogeneous of degree 3 and the d. e. M(x,y)dx+N(x,y)dy = 0 ishomogeneous, then N(x, y) is homogeneous of degree(A) y(B) 0(C) 3(D) 1(E) N(x,y) may not be homogeneous

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Answered: 3. If M(x,y) is homogeneous of degree 3…

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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11. Find the positive integers m such that t?x"+tx'+(t2–m²)x = 0 has a nontrivial solution such that x (0) = 0.
3.c please urgent
2nd order linear homogenous DE with constant coefficients
Let u(x, t) be solution of Utt - Uxx = xt --00 0 u(x, 0) = u:(x, 0) = 0, Then u(2, 3) is equal to (a) 9 (b) 1 (c) 27 (d) 12
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В. Vx [ (A(x,UP) A W(x,Lotto)) – H(x)] V Vy[ (S(x) V L(x)) → A(x.y) ] Vx [ L(x) – W(x,Lotto) ] -S(Isko) A L(Isko) .. H(Isko) where A(x,y): x is accepted at y (y is a university) W(x,y): x wins y S(x): x studied L(x): x is lucky H(x): x is happy
As a specific example we consider the non-homogeneous problem y" + 6y' + 8y = (1) The general solution of the homogeneous problem (called the complementary solution, Yc Ay₁ + By2 ) is given in terms of a pair of linearly independent solutions, Y₁, Y2. Here A and B are arbitrary constants. Find a fundamental set for y” + 6y' + 8y = 0 and enter your results as a comma separated list e^(-2x),e^(-4x) (2) Choose particula Y₁, Y2 in the fundamental set such that the W(x) is positive. Then W (x) 2e^(-6x) U 1 = If your W (x) is negative, then you need to switch your choise of y₁ and y2 and recalculate your W(x). The y₁= e^(-2x) ՂԱԶ √= With this appropriate order we are now ready to apply the method of variation of parameters. -Y₂(x) f(x) W(x) y = Yc + Yp and the y₂2 Y₁(x)f(x) W(x) S [21 dx -cos(e^(2x)) = dx = And combining these results we arrive at = S S e^(-4x) = 2e^(4x)sin(e^(2x)) dx 4 sin(e²x) dx = = = Ур (3) Finally, using A and B for the arbitrary constants in yc, the general solution…
31. Evaluate W (1-x, x, x²) (A) 2 (B) 2r 32. The roots of the auxiliary equation corresponding to the associated homogeneous equation of the DE y"" + 2y" - y' = 10 are (A) m = 0,-1,1 (B) m = 0,1 (multiplicity 2) (C) - 2x (D) -2 (A) Y₁ = C₁e + C₂€¯² + c3 (B) Ye= C₁e²+ C₂xE² + c3 (C) m = 0,-1 (multiplicity 2) (D) m = 1,-1 (multiplicity 2) 33. The complementary solution, ye, of the equation y" + 2y" - y = 10 is (C) Y₁ = ₁₂e (D) Ye=c₁e + c₂e² + c3 + c₂xе¯² + c3
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M O!) 1 where f (x) = defined at the interval [1,4.5] and n=7. COSx+4x اجابتك * Q6) Use LU Decomposition method to solve the sy stem: 6x – y – 4z = 9,3 x + y – 3z = 1.9 x + 2y – z = 3.8 اجابتك خلف يقدم .لا ترسل كلمات السر عبر نماذج جوجل تم إنشاء هذا النموذج داخل جامعة بغداد. بلغ عن سوع معاملة
ax" + bæ' + cx = f(t), x(0) = 0, x'(0) = 0, for time 0 0. Find X(s) L{x(t)} and F(s) = L {f(t)}. X(s) = help (formulas) F(s) = help (formulas) Now find the system transfer function, H(s). H(s) = help (formulas) What will be the output if a Heaviside unit step input ƒ(t) u(t) is applied to the system? New x(t) = help (formulas)

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3. If M(x,y) is homogeneous of degree 3 and homogeneous, then N(x,y) is homogen (A) y (B) 0 (C) 3 (D)