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Given that yy(t) = cost is a solution to y" – y'+y=sint and yz(t) = 3 is a solution to y" – y'+y= 221, use the superposition principle to find solutions to the differential equations in parts (a) through (c) below. (a) y" - y' + y = 20 sint A solution is y(t) = 0
Solve IVP by the Laplace Transform: y" + y = ezt , given y(0) = 0, y'(O) = 1. a) Identify Y(s) = L{y}. 3) Solve for y(t). 8 a) Y (s) = + $2 b) y(t) = } (e2t – cost + 3 sin t) Both of them None of them 3 2+1 +22+1 O a) Y (s) = -2 b) y(t) = e2t - cost + 3 sint
Find the solution of the given initial value problem. y" + 2y' +2y = cost+8(-5); y(0) = 3, y'(0) = 5 ° 20) = us20e" sin + + cost ( +ş) + sint (36+}) x() ==««n6e8cose + cost (3e* +) + sint (80* + }) 20 = usz beé" sin + sing (54* +5.) +cos (34++}) ° 40 = =uaz(Dei* cost + cost ("* + 5 ) + sint (3*+ }) 209 = 192(e“ cose + cost (* +) +sint(****+})
#32 U. + 2y + y + 1 -e: y(0) = 0, y'(o) - 2 In Problems 31-36, determine the form of a particular solution for the differential equation. Do not solve. 31. y" + y = sin : + i cos + + 10' 32. y" - y = 2+ + te? + 1221 x" - x' - 2x = e' cos - + cost y" + 5y' + 6y = sin t - cos 2t 35. y" –...
y(t) is INCORRECT but x(t) is CORRECT DIFFERENTIAL EQUATIONS / Linear Algebra Only people that are proficient in DIFFERENTIAL EQUATIONS should even attempt to solve. No beginners or amateurs allowed. Please write clearly and legibly. No sloppy Handwriting. I must be able to clearly and easily read your solution and answer. Circle final answer. BELOW is an example of what the answer should look very similar to. should be in the same form basically. example 7.10.4 Question Help Use the...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
Solve IVP by the Laplace Transform: y" + y = ezt given y(0) = 0, y'(O) = 1. a) Identify Y(s) = L{y} 3) Solve for y(t). Both of them a) Y (8) 21 + 3 52 +1 $-2 b) y(t) = } (e2t - cost + 3 sin t) 1 3 a) Y (8) 8 g2+1 + $-2 g²+1 b) y(t) = 22 cost + 3 sint None of them
Answer is B If y(t) is the solution of the initial value problem then y(t) =? A. u5(t)e2f sin t B. us(t)e2t+10 sin(t - 5) C. s(t2t-5 sin(2t - 10) 2 D. us(t)e2-5 sin(t - 5) E. ušt)e-2t+10 cos(t-5
A particle moves in the plane with position given by the vector valued function r(t)=cos^3(t)i+sin^3(t)j MA330 Homework #2 particle moves in the plane with position given by the vector-valued function The curve it generates is called an astrid and is plotted for you below. (a) Find the position att x/4 by evaluating r(x/4). Then draw this vector on the graph (b) Find the velocity vector vt)-r)-.Be sure to apply the power and (e) Find the velocity at t /4 by...
Find that solution of the system such that yı(0) = 1, 42(0) = 1. y1 = y1 + y2 + sin() y = 2y1 + cos(t)