1. Find the solution to the IVP : yy - x = 1, y (0) = 2 2. Find the general solution to the exact DE: e* dx – ydy = 0 3. Use ji = cos y to find an EXPLICIT solution to: (tan y)dx + xdy = 0
Problem 1. (5 pt) Find all solutions of (22+1)yy = y2 – 3y + 2.
Q.7, as question above 7. Verify the divergence theorem for F(x, y,z) - by the sphere x2 + y2 + Z2-4. 4xöx +yy +4zőz and V is the region bounded (15 points) 7. Verify the divergence theorem for F(x, y,z) - by the sphere x2 + y2 + Z2-4. 4xöx +yy +4zőz and V is the region bounded (15 points)
462 1.231251937 4 Yy-2(3)(1.061616 237712 4. Given the initial value problem and exact solution: a) Verify the solution by the method of Undetermined Coefficients. x-y+2 y(0)4 ()3e +x+1 (10 points) b) Apply the Runge-Kutta method to approximate the solution on the interval [0.0.5] with step size [15 points h = 0.25 . Construct a table showing six-decimal-place values of the approximate solution and actual solution at each step
rorkyCode.txt x : 5 * 4 - 2; yy : 6! #x; zoo : 120 - X; CA; 10 >A; 20 > A; 30 >A; ; yy > B; 200 > B; Si c; ' wish : 67 zoo * 2; my : 155 ; my >A; wish > C; This final project must be done in Python or C#. Submit source code file(s) on Canvas. Read from the file, rorkyCode.txt, which is a text file that contains codes. The...
- y2 +4, x = 0, y = 0 and y = 2 revolved Find the exact volume of the solid whose region is bounded by x = around the y axis. 61 -6 -4 -2 6 Volume units2
Find the area of the shaded region. Preview x = y2 - 8 y (-55/4, 11/2) x = 3 y - y2
show steps find Domains f (x, y) = arctan (x² + y2-2) x² + y 2 - 1 2 - Cos((x² - 4 ² ) ) cos (x2 + y2))
1) Find the arc length for the following curves. a. y2 = 4(x + 4)3, b. x= 0<x<2 1 sys2 + 4y2 2) Find the surface area resulting from the rotation of the curve about X axis a. 9x = y2 + 18, b. y = V1 + 4x, 2<x< 6 1<x<5 3) Find the surface area resulting from the rotation of the curve about th Y axis. a, y = 1- x2 0 SX S1
Please prove this solution and explain why y2 can be taken as (x^2)(y1) Problem 2. Find the general solution of the equation Note that one of two linearly independent solutions is yi(r) -e. Solution. Using Abel's formula, we get the following relations for the Wronskian dW pi dW 2r1 On the other hand, Comparing these two expression for W(x), we can take y2 :- r2yı. Correspondingly, the general solution is Problem 2. Find the general solution of the equation Note...