4. The two-term perturbation solution to y" = ey?, y(0) = 0, y(0) = 2 on...
1. Find an 1-term perturbation solution of u' + u 1/(1+eu), u(0) = 0,0 <E<< 1 2. Use singular perturbation method to obtain uniform approximation solution to ey"+ (x1)y = 0, y(0) 0, y(1) 1
1. Find an 1-term perturbation solution of u' + u 1/(1+eu), u(0) = 0,0
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Find a two-term perturbation solution of
Find a two-term perturbation solution of
3. (2 pts) The solution of the IVP y = f(y), y(0) = 4 is known to be y(t) = 1+ 9-t. Suppose yz(t) is the solution of the IVP y = f(y), y(2) = 4. Find the solution ya(t).
n : [0, 1] x [0, 1] x [0,1R be the function given by fn (x, y, - (n+3)2 (a) Show that {fnh converges uniformly on [0, 1] × [0, 1] × [0, 1] and find its limit.
n : [0, 1] x [0, 1] x [0,1R be the function given by fn (x, y, - (n+3)2 (a) Show that {fnh converges uniformly on [0, 1] × [0, 1] × [0, 1] and find its limit.
By 5. (a) Verify that y = {24 sin x is a solution to the differential equation dx2 dy + 5y = 0. dc [10 marks) (b) Differentiate the following functions with respect to c: (i) In(1 + sin? 2) (ii) * 2x3 - 4 - 8 dc. (c) Evaluate the integral / 272 * +432 – 4.7" [15 marks] [25 marks] 6. (a) let f: R+R be a function defined by f(x) 3 + 4 if : 51 ax+b...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
(1 point) In this problem you will solve the differential equation (+7)y"+11xy' - y=0. x" for the differential equation will converge at least on the interval (-inf.-sqrt(7)] (1) Ey analyzing the singular paints of the differential equation, we know that a series solution of the form y = . (2) Substituting y = . *" into (x2+7y" + 11xy - y = 0, you get that Multiplying the coefficients in x through the sums E Reindex the sums Finally combine...
2. a. Show that y² + x – 3 = 0 is an implicit solution to dy/dx = -1/(2y) on the interval (-0, 3). b. Show that xy3 – xy: sin x = 1 is an implicit solution to dy_(x cos x + sin x - 1) y 3(x - x sin x) on the interval (0, /2).
Please show all steps for how to solve this perturbation
problem. Thank you.
1. [10 marks] Consider the quadratic equation 2 -0.03x 399 (a) Write this as a perturbation problem. Is it singular or regular? (b) Letting x = ao + aie+ a2e2 + . . . solve up to and including terms of order 0(e2). (c) Compare the solution with the "exact" solution.
1. [10 marks] Consider the quadratic equation 2 -0.03x 399 (a) Write this as a perturbation...
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0