5. Solve the problem Urr +Urx=0, x, y = (0, π), u(0, y) = u(π, y) = 0, u(x, 0) = sin 5x2 sin 3x, u(x, T) = 0.
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- A particular solution of y" + y = sinx + xcosx -(x²sinx – 2xcosx) 4 a. b. (x?sinx – xcosx) 4 (x?sinx + xcosx) C. (x?sinx - 2xcosx) d. 글 2x3sinx-xcosx) е.2) y = sin(3x2e X)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' =0
- find all values of unknowns which satisfy the following equations: 1. (x, y, z) - 3(-1, 2, I) = (0, 0, 0) 2. 7(2, x, x^2)-5(2 -x, x^2) = (1, 12x, x^2)+3(1, 0, 1) 3. (sin x, sin2x, lne) = (sinπ, 2sinx, secx) cosx 4.for the given vectors find the value of U V ad normalise U+V U =(1, 1, 3) V = (3, 1, 1)Caculate both Parts a) y''-2y'-3y=x+1 b) y''+4y=sin3xIf x²y" + xy' + (x² – v = 0 i sinx x>0 ,V1=x and y = y,v. Which of the following equations satisfied by v Select one: a. 1 (x -Esinx)v" + (2x2 cosx)v' = 0 b. (x sinx)v" + (2x 2 cosx)v' = 0 C. 1 (x sinx)v" + (2x¯cosx)v=0 2 cosx)v = 0 d. cOSx-xsinx + x? sinx)v' = 0 3 1 (x 2 sinx)v" + (2x ? cosx- x sinx + x 2 sinx)v' = 0
- 6. x' - x? =t, x(0) = -2, 0, 2; x(2) = 0; x(2.5) = -3, 0, 3 7. y'= sin(yx), y(0) = 0.5, 1,1.5, 2, 2.5 Use Mathematica or Geogebra apps to answer these questions.If x*y' + xy' + (x? - +)v=0 x² - v=o x>0 ,V1=X 2 sinx , and y=y,v. Which of the following equations satisfied by v Select one: а. 1 3 (x Z sinx)v" + (2x cosx-x 2sinx +xZ sinx)v' = 0 2 sinx + x2 sinx)v' = 0 b. (x Zsinx)v" + (2x cosx)y=0 C. 1 (x 2 sinx)v" + (2x2 cosx)v' = 0 d. 1 Zsinx)v" + (2x (x cosx)v' = 0Q4) Find the complete solution of the following equations: (15) b) a) y" +3y' = sin x + 2 cos x (D¹+2D³-3D² - 4D + 4) y = ex -2-3 +4+4 1+2-3-4+4
- '15 JX 30x-x² 9√x²+y2 dydx =29, given in terms of x and y for an Implicit Equation of y2+ x2 = siny + 4 RMI 18) Find y'= A) 2y/(2x - sin y) C) - 2x/(2y - cos y) B) 2x/(2y - cos y) D) - 2y /(2x - sin y) 19) Find an equation of the tangent line y = mx + b to an Implicit Equation of y2+ x2 = siny + 4 at the point (2, 0). A) y = - 2x +4 B) y = 2 x- 4 C) y = - 4x + 6 D) y = 4x - 8 1.5 20) Find (e sin x) dx = by Using TI-Calculator. A) 0. 412 B) 0. 698 C) 1. 573 D) 2. 912 2Find the solution. y'= 1 + 3ytanx A 3y cot³x=ctanx + 3sinx – - sin³x 3y tanx=c+3sinx – cos³x (c) 3y cos³x=c+3sinx – sin³x 3y sin³x=c+ 3cosx – sin³x