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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
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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)