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Show that the following nonlinear system has 18 solutions if
[Hint: Begin by making the substitutions x = sin α, y = cos β, and z = tan γ.]
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- A system x'=Ax has the solutions cos (t) (c() a and sin (t) -cos (t) sin (t) Which of the following is also a solution? O a) O O b) O c) O d) -2 sin (t) 2 cos (t) sin (t) + cos (t) 4 sin (t)- 2 cos (4 (t)) (t) 2 sin (t) + 3 cos (t) -sin (t) os (t)) 2 sin (t) + cos (t) 4 sin (t)- 3 cos (t)arrow_forwardWhich of the following is a correct form of a particular solution of y" + 3y - 4y = 3 cos (2t)e² + 2t² ? Oyp = A cos (2t) + B sin(2t) + Cett + Dt² + Et+F Ур О Ур Yp = A cos (2t) + Bet + Ct² + Dt + E Yp = A cos(2t) + Bet + Ct² Yp = t(A cos(2t) + Bet + Ct²) | Yp = t² (A cos(2t) + Bet + Ct² + Dt + E) O yp= Yp = t(A cos(2t) + B sin(2t) + Cett + Dt² + Et+F)arrow_forwardFind the general solution (D2 + 9)y = 5e*- 162x %3D a. y = C1 cos 3x + c2 sin 3x + 18x+ex b. y = c cos 3x+ c2 sin 3x 18x+ ex C. y C1 cos 3x + C2 sin 3x- 18x2 +ex d. y = c1 cos 3x+ c2 sin 3x + 18x2 + e. none of these 112 DIarrow_forward
- Look for the annihilator of the given expressions. i) e2x sin3x ii) x³ e4x iii) 5x* - 2.x + 8x - 7 iv) x³ e4x cos2xarrow_forwardFind the general solution (D? + 9)y = 5e* - 162x a. y = C1 cos 3x + c2 sin 3x + 18x +e* 2 b. y = c1 cos 3x + c2 sin 3x – 18x+e C. y = c1 cos 3x + c2 sin 3x - 18x2 + e* 2 d. y = c, cos 3x + c2 sin 3x + 18x² + 2 e. none of these 1/2arrow_forwardWhat is the particular solution of the function xe8# – 2 sin 2x – e2¤ cos 3x? O Aešr + Bre& + C cos 2x +E sin 2x + Fe2 cos 3x + Ge2" sin 3x O Are&z + B cos 2x + C sin 2x + Ee2" cos 3x + Fe2 sin 3x O Aešr + Bre& + Ce2" cos 2x + Ee2 sin 2x + Fe2 cos 3r + Ge2" sin 3x O Axesr + C sin 2x + De2 cos 3xarrow_forward
- Solve one of the following deferential equations a) rsine de + (r³2r² cose + cose)dr = 0. b) (xy + y)dx + 2(x² y² +x+y)dy = 0arrow_forwardWhich of the following equations does not hold for all values of x and y? cos(r + y) = cos(x) cos(y) – sin(x) sin(y) sin(2x) = 2 sin(x) cos(x) sin? æ + cos (x) =1 sin(-a) = - sin(x) sin(x + y) = sin(x) + sin(y)arrow_forwardWhat is the general solution of (D® + 20D4 + 100D²) y y = C1 + C2æ + (C3 + C5 x) cos V10x + (C4 + C6x) sin v10x %3D C1 + (C2 + C4x) cos 10x + (C3 + C5x) sin 10x y = C1 + C2x + (C3 + C;x) cos 10a + (C4 + C6x) sin 10a y = C1 + (C2 + C4x) cos V10x + (C3 + C5æ) sin v10xarrow_forward
- Determine the solutions of the following first-order ODEs: Tip:y'=xv'+v y=xv * xv'+v=(4xv-3x)/(2x-xv) >>>> xv'+v=(2v-3)/(1-v)>>>xv'=(2v-3-v+v²)/(1-v) * ANSWER CORRECT :|y − x| = C|y + x|3 Any different answer will be considered wrongarrow_forward5. It is given that two linearly independent solutions of a²2y" + xy + - y=0, x>0 are æ-1/2 sina and -1/2 cos z. Find the general solution of 2²³y² + xy² + (2²_ -) v = 50²4/²4 2 sinz, x>0.arrow_forwardSuppose that the position of one particle at time t is given by the equations X₁ and y₁. Meanwhile, the position of a second particle is given by the equations x₂ and y₂. x1 = 4sin(t) Y₁ = 2cos(t) 0 ≤t≤ 2n x₂ = -4 + cos(t) Y2 = 1 + sin(t) 0 ≤t≤ 2π (a) Graph the paths of both particles. (Do this on paper. Your instructor may ask you to turn in this work.) How many points of intersection are there? (b) Find the collision point, where the particles are at the same place at the same time. (c) If the x-coordinate of the second particle is given by x₂ = 4 + cos(t) instead, is there still a collision? O Yes O Noarrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education
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