(a) and (b) solved.
Determine the values of a, if any, for which all solutions of the differential equation y''...
Determine the values of a, if any, for which all solutions tend to zero as t > oo. Also determine the values of a, if any, for which all (nonzero) solutions become unbounded as t -> oo: y" (2a 1) a(a - 1)y 0
give a clear amswer with all areps. i have trouble
understanding limits so explain clearly for positive rating
In each of Problems 17 and 18, determine the values of a, if any, for which all solutions tend to zero as t -> oo; also determine the values of a, if any, for which all (nonzero) solutions become unbounded as t oo y" (2a - 1) y a(a - 1) y = 0 17.
In each of Problems 17 and 18,...
(1 point) Determine the two singular points of the differential equation (x2-49)y" + (7-x)y' + (r' + 14x + 49)y-0 List the points in increasing order: Xi = X2 Which of the following statements correctly describes the behaviour of the solutions of the differential equation near the singular point x A. All solutions remain bounded near xi. B. All non-zero solutions are unbounded near C. At least one non-zero solution remains bounded near x and at least one solution is...
i) Find all values of a for which all solutions of the differential equation y/ar 2)y = 0, x0 approach zero as x -+ 0.
i) Find all values of a for which all solutions of the differential equation y/ar 2)y = 0, x0 approach zero as x -+ 0.
. 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
Determine the values of r for which the differential equation t2y′′−6ty′+6y=0 has solutions of the form y=tr for t > 0
7: Problem 6 Previous Problem List Next (1 point) Determine the two singular points of the differential equation (x2-16)y (4 - x)y +(x2 + 8x+ 16)y = 0 List the points in increasing order: X Which of the following statements correctly describes the behaviour of the solutions of the differential equation near the singular point X1 A. At least one non-zero solution remains bounded near x1 and at least one solution is unbounded near X1 . B.All solutions remain bounded...
A population is modeled by the differential equation Find all values of Pfor which the population is increasing. 00< P < 4300 Oo<P<1.4 OP>1.4 P> 4300
Consider the following differential equation. 6xy" + 7xy' + 13e+y=0 (a) Find all the regular singular points of the given differential equation. If necessary, enter your answers separated by commas. 2= QC (b) Determine the indicial equation and the exponents at the singularity of each regular singular point. Enter the values of ry and r2 in increasing order. Fr) QC T1 = 12 QC Click if you would like to Show Work for this question: Open Show Work
Consider the differential equation y' (t) = (y-4)(1 + y). a) Find the solutions that are constant, for all t2 0 (the equilibrium solutions). b) In what regions are solutions increasing? Decreasing? c) Which initial conditions y(0) = A lead to solutions that are increasing in time? Decreasing? d) Sketch the direction field and verify that it is consistent with parts a through c. a) The solutions are constant for (Type an equation. Use a comma to separate answers as...