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8.2 (2). Consider the linear equation Y'(x) = XY (2) + (1 - 1) cos(x) -...
8.2 (2). Consider the linear equation Y'(x) = XY (2) + (1 - 1) cos(x) - (1+) sin(x), quady (0) = 1 The true solution is Y (1) = sin(1) + cos(r). Solve this problem using Euler's method with several values of and h, for 0 <<<10. Comment on the results. (a) X = -1; h=0.5, 0.25, 0.125 (b) X = 1; h = 0.5, 0.25, 0.125 (c) = -5; h=0.5, 0.25, 0.125, 0.0625 (d) = 5; h= 0.0625
Consider the linear equation Y ′(x) = λY (x) + (1 − λ) cos(x) − (1 + λ) sin(x), quadY (0) = 1 . The true solution is Y (x) = sin(x) + cos(x). Solve this problem using Euler’s method with several values of λ and h, for 0 ≤ x ≤ 10. Comment on the results. (a) λ = −1; h = 0.5, 0.25, 0.125 (b) λ = 1; h = 0.5,0.25,0.125 (c) λ = −5; h = 0.5,...
Consider the homogeneous linear third order equation A) xy'''−xy'' + y'−y = 0 Given that y1(x) = e^x is a solution. Use the substitution y = u*y1 to reduce this third order equation to a homogeneous linear second order equation in the variable w = u'. You do not need to solve this second order equation. B.) xy''' + (1−x)y'' + xy'−y = 0. Given that y1(x) = x is a solution. Use the substitution y =...
please solve the given differential equation 11. [y cos(xy) sin x] dx +xcos(xy) dy 0
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given D2y + 25y = -5 sin 5x (Let y p = Ax sin 5x + Bx cos 5x.) sin 5x + c2 cos 5x + x sin 5x - 1 x cos 5x Oo oo cos 5x + = x cos 5x y = C1 sin 5x + C2 cos 5x + 5x sin 5x y = C1 sin 5x + C2 cos 5x...
6. Solve the initial value problem y" + y = 0, y(0)=0, y'0=1 (a) -COS X (b) -sin x (c) -sin x + cos x (d) -sin x COS X (e) COS X (f) sin x (g) sin x-COS X (h) sin x + cos x 7. Find a particular solution yn of the differential equation (using the method of undetermined coefficients): y + y =p2 (a) 2e (b) 3e (c) 4e: (d) 6e (e) 2/2 (f) e2/3 (g) e2/4...
A solution to the differential equation _ cot(ay)-ry a. x cos(xy) = constant b. x sin(xy) = constant c. y cos(xy) = constant d. ysin(xy) = constant
Consider the differential equation: (7y sin(xy) + 2 sec x) dx = (2 lny – 4x sin(xy))dy Note: Do not use square brackets in your response, use normal parantheses if you have to, i.e "0" Then aM ду and ƏN ax Is this equation exact? Yes No Consider the differential equation: sin(x)dx + 5y cos(x)dy = 0 Which of the following can be an integrating factor to make the equation exact? Select all that apply. On=e-54 On=tan(x) Ju=e-542/2 On =...
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0 4. (a Let (sin( x cos( ) dr...