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(1) In the following initial value problems, the number a is a real param- eter. Determine...
please show all your work . (6 points) Of the four initial or boundary value problems below, ouly one is guaranteed...
please show all your work
. (6 points) Of the four initial or boundary value problems below, ouly one is guaranteed to have a unique solution according to the Existence and Uniqueness Theorons. Which one i i (a) ty"-Py, + e'y = ), y(1)s 0, V(1) = T. tan (f (b) ty" + 2/-3y = 0, y (0)0. y(0) = 2, y(5) = 0. (d) V, + sec(t)y = sin(2t),
. (6 points) Of the four initial or boundary value...
Determine which of the following initial value problems is correctly associated to the longest interval guaranteed...
Determine which of the following initial value problems is correctly associated to the longest interval guaranteed by the existence and uniqueness theorem. y O [0, 4); ty" = 0, y(1) = 0, y (1) = -2 O (5,00); (x – 5)3 dy – 3(x + 2)2 dy CU 3+3 v(2) = -1,v' (2) = 1 1 d.c3 dx2 0(-1,1); 2(t– 1)y" + 3ty - y=et, y(0) = 1, y (0) = 0 (-0,3); xạy" + 2xy – y = 713,...
In the following problems determine whether existence of at least one solution of the given initi...
In the following problems determine whether existence of at least one solution of the given initial value problem is thereby guaranteed and if so, whether the uniqueness of that solution is guaranteed. For each initial value problem determine all solutions and the intervals where they hold, if the case. (a) dy/dx = y^(1/3); y(1) = 1. (b) dy/dx = y^(1/3); y(1) = 0. (c) dy/dx =sqrt(x - y); y(2) = 1. Can you explain how can we approach these kind...
26 Find the solutions of the following initial-value problems: (a) cos(x + t)| _ + 1...
26 Find the solutions of the following initial-value problems: (a) cos(x + t)| _ + 1 | + 1 0, x(0) π 3 (b) 3(x + 2012ー+ 6(x +21)]/2 + 1 = 0. dt x(-1) 6
1. (Review of initial/boundary value problems for ordinary differential equations) Determine u(x), a the solutions, if...
1. (Review of initial/boundary value problems for ordinary differential equations) Determine u(x), a the solutions, if any, to each of the following boundary value problems. Here, u function of only one variable. u', _ 411, + 1311 = 0, 11(0) = 0 u(π) = 0 u', + 511,-14u = 0 11(0) = 5 11,(0) = 1 0<x<π 11" + 411, + 811 = 0, (0)0 11(x) = 0 0 < x < π 11(0)=0 11(2n) = 1 11" +" u-0,...
4.2.3. Write down the solutions to the following initial-boundary value problems for the wave equ...
I
need help with this PDE problem, part A and D
4.2.3. Write down the solutions to the following initial-boundary value problems for the wave equation in the form of a Fourier series: a) utt = uzz , u(t, 0) = u(t, π) = 0, u(0,x) = 1, ut(0,z) = 0; (b) utt = 2uxx, a(t, 0) = u(t, π) = 0, a(0,x) = 0, ut(0,x) = 1; c) utt = 3uzz , ti(t, 0)=u(t, π)=0, u(0,x) = sin3 x,...
Special Functions- IVP and BVP Quiz 3.12 Solve the following initial value problems. Ans: y- cost...
question 1,2,3 please
Special Functions- IVP and BVP Quiz 3.12 Solve the following initial value problems. Ans: y- cost+ H(-3)-cos(t 2r) H(t3) y(0)=0,s(0)=1 where 2. v', +y=g(t), { 1, 0 t<π/2 g(t) = Ans:y=1-cos t + sin t + (sint-1)H(t-π/2) x(0) = 0,d(0) = 1 where 3、z"(t) + 162(t) = g(t), cos 4t, 0 12π. t<π 5
Special Functions- IVP and BVP Quiz 3.12 Solve the following initial value problems. Ans: y- cost+ H(-3)-cos(t 2r) H(t3) y(0)=0,s(0)=1 where 2. v',...
Consider the initial value problem x^2 dy/dx = y - xy, y(-1) = 1 Use the...
Consider the initial value problem x^2 dy/dx = y - xy, y(-1) = 1 Use the Existence and Uniqueness theorem to determine if solutions will exist and be unique. Then solve the initial value problem to obtain an analytic solution.
2y 1. (9 points) Given the initial value problem y' = y (xo) = yo. Use...
2y 1. (9 points) Given the initial value problem y' = y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where x, 60, b) no solution exists if y(0) = % 70, and c) an infinite number of solutions exist if y(0) = 0.
B=1 1. Consider the following initial value problem. V = n(1 + y²), OSI31 y(0) =...
B=1 1. Consider the following initial value problem. V = n(1 + y²), OSI31 y(0) = 0+1 a) ( 15p.) Determine the existence and uniqueness of the solution. b) ( 15p.) Use Euler's method with h = 0.25 to approximate the solution at t=0.5. 2=8
please show all your work
. (6 points) Of the four initial or boundary value problems below, ouly one is guaranteed to have a unique solution according to the Existence and Uniqueness Theorons. Which one i i (a) ty"-Py, + e'y = ), y(1)s 0, V(1) = T. tan (f (b) ty" + 2/-3y = 0, y (0)0. y(0) = 2, y(5) = 0. (d) V, + sec(t)y = sin(2t),
. (6 points) Of the four initial or boundary value...
Determine which of the following initial value problems is correctly associated to the longest interval guaranteed by the existence and uniqueness theorem. y O [0, 4); ty" = 0, y(1) = 0, y (1) = -2 O (5,00); (x – 5)3 dy – 3(x + 2)2 dy CU 3+3 v(2) = -1,v' (2) = 1 1 d.c3 dx2 0(-1,1); 2(t– 1)y" + 3ty - y=et, y(0) = 1, y (0) = 0 (-0,3); xạy" + 2xy – y = 713,...
26 Find the solutions of the following initial-value problems: (a) cos(x + t)| _ + 1 | + 1 0, x(0) π 3 (b) 3(x + 2012ー+ 6(x +21)]/2 + 1 = 0. dt x(-1) 6
1. (Review of initial/boundary value problems for ordinary differential equations) Determine u(x), a the solutions, if any, to each of the following boundary value problems. Here, u function of only one variable. u', _ 411, + 1311 = 0, 11(0) = 0 u(π) = 0 u', + 511,-14u = 0 11(0) = 5 11,(0) = 1 0<x<π 11" + 411, + 811 = 0, (0)0 11(x) = 0 0 < x < π 11(0)=0 11(2n) = 1 11" +" u-0,...
I
need help with this PDE problem, part A and D
4.2.3. Write down the solutions to the following initial-boundary value problems for the wave equation in the form of a Fourier series: a) utt = uzz , u(t, 0) = u(t, π) = 0, u(0,x) = 1, ut(0,z) = 0; (b) utt = 2uxx, a(t, 0) = u(t, π) = 0, a(0,x) = 0, ut(0,x) = 1; c) utt = 3uzz , ti(t, 0)=u(t, π)=0, u(0,x) = sin3 x,...
question 1,2,3 please
Special Functions- IVP and BVP Quiz 3.12 Solve the following initial value problems. Ans: y- cost+ H(-3)-cos(t 2r) H(t3) y(0)=0,s(0)=1 where 2. v', +y=g(t), { 1, 0 t<π/2 g(t) = Ans:y=1-cos t + sin t + (sint-1)H(t-π/2) x(0) = 0,d(0) = 1 where 3、z"(t) + 162(t) = g(t), cos 4t, 0 12π. t<π 5
Special Functions- IVP and BVP Quiz 3.12 Solve the following initial value problems. Ans: y- cost+ H(-3)-cos(t 2r) H(t3) y(0)=0,s(0)=1 where 2. v',...
2y 1. (9 points) Given the initial value problem y' = y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where x, 60, b) no solution exists if y(0) = % 70, and c) an infinite number of solutions exist if y(0) = 0.
B=1 1. Consider the following initial value problem. V = n(1 + y²), OSI31 y(0) = 0+1 a) ( 15p.) Determine the existence and uniqueness of the solution. b) ( 15p.) Use Euler's method with h = 0.25 to approximate the solution at t=0.5. 2=8
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