dx Consider the system 2 - NICO ху 2 22 dy dt = 2y – 1- 2XY dt 2 (a) Identify all critical points of the system. (b) For each critical point, use eigenvalues to classify the critical points according to stability (stable, unstable, asymptotically stable) and type (saddle, proper node, etc).
2.3.13 3 of 42 Obtain the general solution to the equation у dx dy + 6x = 4y3 С The general solution is x(y) = on IN 74 + ignoring lost solutions, if any. 16
show all work and i'll thumbs up Solve dy dx -у Xe
2. Given two initial value problems, у" — р(г)у +q()у +r(x) with a <I<b,y(a) — с,1 (а) —0 (1) and у" — р(г)у + g(х)у with a < r <ь,y(a) — 0, and / (а) — 1 (2) [a, b) where p(x), q(z) and r(x) Show that given two solutions yı(x), y2(x) to the linear value problems above, (1) and (2), respectively, then there exists a solution y(x) to a linear boundary value problem above where y(a) %3D 0, у...
QUESTION 11 +3x Solve the first-order differential equation dy e2y2 = dx у
02: Use Euler's Method dy = ху
1 VMware Horizon Sketch the region of integration. Vy cos(y) dy dx (1/8 у 2) 2 6 8 2 4 6 O 8 8H 6 2 4 Eva uate the trated Integra, switching the order of integration if necessary COSTS sin 8-1 Type here to search o *
Compute Ay and dy for the given values of x and dx - Ax. (Round your answers to three decimal places.) y - 2x - x2, x-2, Ax - -0.4 Ay - dy - Sketch a diagram showing the line segments with lengths dx, dy, and Ay. у 31 2 23- dy wy sy dy - 1 3 -1 a o -1 2 2 dy dy ay -1
Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise. ху 7 In(7 + y) dx - dy, where C is the triangle with vertices (0,0), (4,0), and (0,8) fe 7+ y ху f 7 ln(7 + y) dx – dy = 7+y
x= Jy=X Show that | * (x+3y) dy dx = [ { « + 3) dx dy + m2 L); *+ 3ydr dy (x + 3y) dx dy + (x + 3y) dx dy Jy=1 Jx=y2