Solve the 1-dimensional heat equation problem. ди J²u = Ət მე2 ди ди (0, t) = (1,t) = 0, for t> 0 Əx მე u (x, 0) = f(x) = 54 cos (2πx) + 3 cos (6πx), for 0≤ x ≤ 1
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- solve xsinydx+(x2+1)cosydy=0Suppose that a particle moves according to the law of motion s = t² - 12t+24, (A) Find the velocity at time t. v(t) (B) What is the velocity after 3 seconds? = ₺≥ 0. Velocity after 3 seconds = (C) Find all values of ₺ for which the particle is at rest. (If there are no such values, enter 0. If there are more than one value, list them separated by commas.) t = (D) Use interval notation to indicate when the particle is moving in the positive direction. (If the particle is never moving in the positive direction, enter "{}" without the quotation marks.) Answer =Find all solutions of the equation in the interval [0, 21). (14 cos x-7)(9 cos x) = 0 O A. 0, TC 6' 6 元 T 5T 3T О в. 6' 2'6'2 TC Ос. 0, 元, 3' 3 ITC T 3t 5T O D. 3' 2' 2'3 3.
- If x*y" + xy' + (x? -)y=D x >0 ,V1=x 2sinx and y = y,v. Which of the following equations satisfied by v Select one: a. (x 2 sinx)v" + (2x 2 cosx)v' = 0 b. (x 2sinx)v" +(2x 2 cosx)v=0 C. (x2sinx)v" + (2x cosx – xsinx + x2 sinx)v' = 0 cosx - x 2 sinx + x 2 sinx)v' = 0 d. (x 2 sinx)v" +(2x2 cosx)v' =0Find all solutions of the equation in the interval [0, 2x). cos 2x = T 3n 57 7n OA. 4' 4 - - - 4 4 п 7л 9т 151 OB. 8' 8' - - ' 8 2n О С. 0, T, 3 3 - O D. ØConsider the equation "+7+10y=9e5+2 cos(x). a. Find the solution of the complementary equation. Use A and B for the coefficients. Y₁(z) = b. Find the general solution set for "+7y+10y=9e5+2 cos(z). Separate items by commas.
- Determine exact solutions for the equation 2sin'x – 3sinx + 1 = 0 in the interval x Ï [T, 3n].Find general solution, y., and particular solution y, of the following: (only solve for coefficient of 2) а. у" - Зу" + 2y' %3D 4x2 b. y" - Зу' + 2у — 4x?е2х c. y" + 16y = 10 sin 4xQ3) Find the root of the equation F(x)=x² - 3(sinx)² by using Newton Raphson method with initial value of Xo-6. Take for i= 1.2.3