Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. dy 3-y ах WNAHRI -2 2 A) y-Cln(3-y) B) y-3+Ce D) y Cln(y-3) E) y 3x+Ce "Х...
Solve the differential equation. dy dx 3.c2e- y=In(x3 + C) y=Cln(x) y=+*+ Oy=ln(3x + C)
1) Separate variables and find the particular solution of the differential equation x2 dy = y dx if y = 1 when x = 1. -1 - + 2 A) In y = =-- + 2 or y=e B) In y = ln x2 or y = x2 A) in y=- +2 or y=e**2 C) In y=-1+1 or w ts - +1 In y = -— +1 or y=e D) 4+2 or y= 2: 2) Find the general solution of...
The slope field for the equation y'=-x+y is shown above On a print out of this slope field, sketch the solutions that pass through the points (i) (0,0); (ii) (-3,1); and (iii) (-1,0). From your sketch, what is the equation of the solution to the differential equation that passes through (-1,0)? (Verify that your solution is correct by substituting it into the differential equation.)
32 111 8. Shown above is a slope field for the differential equation d dy 2 4 v2 If y - g(r) is the solution to the differential equation with the initial condition g(-12 ,then lim slx) =-1, then lim g(x) is (B) -2 (C) 0 (D) 2 (E) 3 32 111 8. Shown above is a slope field for the differential equation d dy 2 4 v2 If y - g(r) is the solution to the differential equation with...
Find the general solution for the differential equation. x dy/dx + 3y = 4x2 – 3x; x>0 y=_______
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) arctan() (d) List all equilibrium solutions of the differential equation, and classify the stability of each: V = y(y - 6)(n-10) (e) Use equilibrium solutions and stability analysis...
Determine the slope field for the differential equation. Use the slope field to sketch a particular solution passing through (0,0) and a particular solution passing through (0,3). dy dc (g - 2)(g+2) 4
3. Find the general solution of the differential equation y” + 2y' + y = 0 (a) y=ce' +c,e* (b) y= ce" + xe * (c) y = cxe* +c,e* (d) y= ce* +C,xe" (e) y=ce?* +c,e-2 (f) y= c,e + ,xe” (g) y=cxe?* +cze 2 (h) y= c,e + ,xe 21
The slope field for the equation dy/dx = x+y for −4 ≤ x ≤ 4, −4 ≤ y ≤ 4 is shown in the figure below. The slope field for the equation yxy for -4 SxS4, -4 Sy s4 is shown in the figure below TA (a) Sketch the solutions that pass through the following points: -Select The solution has slope at (0, 0) and is Concave up concave down inear (ü) (-3, 1)increasing The solution sdecreasing -Select concave up...
5. Given the differential equation: e(dy/dx) 2x (a) Find the general solution (b) Graph particular solutions for integration constants C-0, 5, 10 and 15. You can put all plots on one graph or prepare separate plots. Show all calculations 5. Given the differential equation: e(dy/dx) 2x (a) Find the general solution (b) Graph particular solutions for integration constants C-0, 5, 10 and 15. You can put all plots on one graph or prepare separate plots. Show all calculations