9. (8points) Determine and justify whether the set of solutions of the differential equation, and +...
1: Determine whether the given differential equation is exact Q1: Determine whether the given differential equation is exact a) [1 + In(xy)]dx + (dy = 0 소 소 전 소 소 be xydx - (xy2 + y3)dy = 0 t
#13 In Problems 9 21, determine whether the given set of vectors forms a basis for the specified vector space. IR 12 IR 5'8 13 0 16 IR 0 15 IR3 18 17 IR 19 IR
Determine the values of r for which the differential equation t2y′′−6ty′+6y=0 has solutions of the form y=tr for t > 0
a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of the O.D.E.? C) State the general solution for this O.D.E. a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of...
Determine the values of a, if any, for which all solutions of the differential equation y'' – (2a – 9)y' + (a? – 9a + 14)y = 0 tend to zero as t → 00; also determine the values of a, if any, for which all (nonzero) solutions become unbounded as t → . Solutions tend to zero as t + op as long as a (Click for List) A QE Solutions become unbounded as t → as long as...
. 0-1 polnts BoyceDIE010 1.3020. Determine the values of r for which the given differential equation has solutions of the form y for t>o . -11 points BoyceDiffEQ10 1.3.020.GO Determine the values of r for which the given differential equation has solutions of the form y- for t>o
1-1 0 / x has a basis 7. Recall that the vector space of solutions to the 10 -1). differential equation x = ( of solutions Yr(t), x2(t) where 41 (0) = (0) and Tet 420) = 1 9). Another basis is xi(t) = ( Xi) + -e xz(t) = (-+). Express Vi(t), «z(t) as linear combinations of xi(t), x2(t).
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y +3z 0. Let L be the set of solutions of the inhomogeneous linear equation (a) Define affine subspace of a vector space. (b) Prove that L is an affine subspace of R3 (c) Compute a vector v such that L = v + W (6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y...
Find the general solution of the given differential equation, and use it to determine how solutions behave as t → 0. y + 7y = t+e-5t QC. 0 Solutions converge to the function y =
6. Consider the autonomous differential equation (a) Find all of its equilibrium solutions. (b) Classify the stability of each equilibrium solution. Justify your answer. (c) If y(t) is a solution that satisfies y(-1) =-4, what is y(0)? Without solving the equation, briefly explain your conclusion. (d) If y() is a solution that satisis y(3) -3, then what is lim y(t)? 6. Consider the autonomous differential equation (a) Find all of its equilibrium solutions. (b) Classify the stability of each equilibrium...