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3. Use the Maximum/Minimum Principles to deduce that...
2. Use eigenfunction expansion to solve the following IBVP: please answer v) (fifth one) 2. Use...
2. Use eigenfunction expansion to solve the following IBVP:
please answer v) (fifth one)
2. Use eigenfunction expansion to solve the following IBVP u,(x.t)-u(x.t)+(t-1)sin(a) 0<x<1 t>0 u(0,t)0, u(l,r) 0, t>0 u,(x,t)(x) cos(z), 0 <x<1 t>0 n(x,0) = 2-cos(32t) 0 < x < 1 u(0,0, u(l,t) 0, t>0 n(x,0) = 1 u,(x,0) = 0 0 < x < 1 IV Hm(x,y)+u" (x,y)--r', 0<x<1 0<y<2 u(x,0) = 0, u(x2) =-x 0 < x < 1 v) 7" 11(0,8) bounded , -π<θ<π
Just need the answer and no steps. The solution of the heat equation Uxx = U7,...
Just need the answer and no steps.
The solution of the heat equation Uxx = U7, 0 < x < 2,1 > 0, which satisfies the boundary conditions u(0, t) = u(2,t) = 0 and the initial condition u(x, 0) = f(x), (1, 0 < x < 1 L where f(x) = 3 }, is u(x, t) = į bn sin (n7x De 7 ,where bn = 10,1 < x < 2 S n=1 Select one: o a [(-1)] o...
Please show all work and answer all parts with an original solution. Find the solution rt)...
Please show all work and answer all parts with an original
solution.
Find the solution rt) for the following 1-D heat oquation with homsgensous boundary condiions: au t > 0 u(0, t) 0, t >0 t>0, u(z,0) = 5 sin(2x)-14 sin(3x), Are there infinitely many terms in the solution for this initial boundary value problem? How many non-zero terms comprise the solution?
03: Find the absolute maximum and minimum values of f(x) = sin x + cos x...
03: Find the absolute maximum and minimum values of f(x) = sin x + cos x on the interval 26). [5] 2 $ty) = OSX - Tin x = 0 V 2 f(t) = -1 (27) = ? absolt minum X Q4: Consider the function g(x) = *°+2 a) State the domain of g(x) (- 0,0)u(0,0) b) Intercepts, if any lx Rob at x=1,1 at $850 941) = 3 9(-1) 1,3) and 1-1,-1)) tunarnnine whether n has any acvmntotes and...
3. In the problems below, you may use the formal solution of the appropriate partial differential...
3. In the problems below, you may use the formal solution of the appropriate partial differential equation and boundary conditions from course notes and the text. You do not have to derive the formal solution. (a) (15 points) Find the solution of the initial-boundary value problem du du ət – Ər2 t> 0, 0 < x <7, u(0,t) = , t>0, u( ,t) = 0, t>0, u(x,0) = sin 2x, 0<x< 7. (b) (10 points) Solve the initial-boundary value problem...
1. Find the absolute maximum and absolute minimum values of the given functions on the given inte...
1. Find the absolute maximum and absolute minimum values of the given functions on the given intervals. You do not need to explain your solution with sentences (a) u(z) = er_ 2x on the interval [0, 1]. (b) h(x)- on the interval [0, 3]. Note that you will have to use a logarithmic derivative (as we have done in class) to compute h'(x). You might need a table to compute h(O0)
1. Find the absolute maximum and absolute minimum values...
please I need solution as soon as possible Q2 Given the following heat conduction initial-boundary value...
please I need solution as soon as possible
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = uti 0<x< 6; t>0; B.C.: uz (0.t) = 0; ux(6,t) = 0; t> 0; 1. C. :U(x,0) = 12 + 5cos (6x) – 4cos(2x); 0<x<6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (6) Determine whether the boundary...
Problem #4: Use separation of variables to find a product solution to the following partial differential...
Problem #4: Use separation of variables to find a product solution to the following partial differential equation, Ou (5y + 8) ou си + (3x + 6) oy = 0 that also satisfies the conditions u(0,0) = 9 and ux(0,0) = 8. Problem #4: Enter your answer as a symbolic 9*e^(1/9)*(3*x^2/2+6*X-5*y^2/2-function of x,y, as in these examples + 6x - 9e1/9(3 + 52 - 8y) Just Save Submit Problem #4 for Grading Problem #4 Attempt #1 Attempt #2 Attempt #3...
Help please and circle the answer to the blank problem and make it clear and visible....
Help please and circle the answer to the blank problem and make
it clear and visible. Ive also included a similar problem so you
know what the answer should look like. Thanks
Evaluate. Assureu > when in u appears. (Hint: Use the properties of logarithms.) Inx? (Type an exact answer.) Evaluate. Assume u> 0 when in u appears. (Hint: Use the properties of logarithms.) x10 Substitute for In x und du for dx in the integral Inx -dx= Integrale with...
4. Consider the semi-infinite string problem given by Utt = cʻuza, 0<x< 0,> 0 u(x,0) =...
4. Consider the semi-infinite string problem given by Utt = cʻuza, 0<x< 0,> 0 u(x,0) = f(x), 0<x< ~ ut(2,0) = g(2), 0 < x < 0 u(0,t) = 0, t> 0 Suppose that c=1, f(0) = (x - 1) - h(2 – 3) and g(C) = 0. (a) Write out the appropriate semi-infinite d'Alembert's solution for this problem and simplify. (b) Plot the solution surface and enough time snapshots to demostrate the dynam- ics of the solution.
2. Use eigenfunction expansion to solve the following IBVP:
please answer v) (fifth one)
2. Use eigenfunction expansion to solve the following IBVP u,(x.t)-u(x.t)+(t-1)sin(a) 0<x<1 t>0 u(0,t)0, u(l,r) 0, t>0 u,(x,t)(x) cos(z), 0 <x<1 t>0 n(x,0) = 2-cos(32t) 0 < x < 1 u(0,0, u(l,t) 0, t>0 n(x,0) = 1 u,(x,0) = 0 0 < x < 1 IV Hm(x,y)+u" (x,y)--r', 0<x<1 0<y<2 u(x,0) = 0, u(x2) =-x 0 < x < 1 v) 7" 11(0,8) bounded , -π<θ<π
Just need the answer and no steps.
The solution of the heat equation Uxx = U7, 0 < x < 2,1 > 0, which satisfies the boundary conditions u(0, t) = u(2,t) = 0 and the initial condition u(x, 0) = f(x), (1, 0 < x < 1 L where f(x) = 3 }, is u(x, t) = į bn sin (n7x De 7 ,where bn = 10,1 < x < 2 S n=1 Select one: o a [(-1)] o...
Please show all work and answer all parts with an original
solution.
Find the solution rt) for the following 1-D heat oquation with homsgensous boundary condiions: au t > 0 u(0, t) 0, t >0 t>0, u(z,0) = 5 sin(2x)-14 sin(3x), Are there infinitely many terms in the solution for this initial boundary value problem? How many non-zero terms comprise the solution?
03: Find the absolute maximum and minimum values of f(x) = sin x + cos x on the interval 26). [5] 2 $ty) = OSX - Tin x = 0 V 2 f(t) = -1 (27) = ? absolt minum X Q4: Consider the function g(x) = *°+2 a) State the domain of g(x) (- 0,0)u(0,0) b) Intercepts, if any lx Rob at x=1,1 at $850 941) = 3 9(-1) 1,3) and 1-1,-1)) tunarnnine whether n has any acvmntotes and...
3. In the problems below, you may use the formal solution of the appropriate partial differential equation and boundary conditions from course notes and the text. You do not have to derive the formal solution. (a) (15 points) Find the solution of the initial-boundary value problem du du ət – Ər2 t> 0, 0 < x <7, u(0,t) = , t>0, u( ,t) = 0, t>0, u(x,0) = sin 2x, 0<x< 7. (b) (10 points) Solve the initial-boundary value problem...
1. Find the absolute maximum and absolute minimum values of the given functions on the given intervals. You do not need to explain your solution with sentences (a) u(z) = er_ 2x on the interval [0, 1]. (b) h(x)- on the interval [0, 3]. Note that you will have to use a logarithmic derivative (as we have done in class) to compute h'(x). You might need a table to compute h(O0)
1. Find the absolute maximum and absolute minimum values...
please I need solution as soon as possible
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = uti 0<x< 6; t>0; B.C.: uz (0.t) = 0; ux(6,t) = 0; t> 0; 1. C. :U(x,0) = 12 + 5cos (6x) – 4cos(2x); 0<x<6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (6) Determine whether the boundary...
Problem #4: Use separation of variables to find a product solution to the following partial differential equation, Ou (5y + 8) ou си + (3x + 6) oy = 0 that also satisfies the conditions u(0,0) = 9 and ux(0,0) = 8. Problem #4: Enter your answer as a symbolic 9*e^(1/9)*(3*x^2/2+6*X-5*y^2/2-function of x,y, as in these examples + 6x - 9e1/9(3 + 52 - 8y) Just Save Submit Problem #4 for Grading Problem #4 Attempt #1 Attempt #2 Attempt #3...
Help please and circle the answer to the blank problem and make
it clear and visible. Ive also included a similar problem so you
know what the answer should look like. Thanks
Evaluate. Assureu > when in u appears. (Hint: Use the properties of logarithms.) Inx? (Type an exact answer.) Evaluate. Assume u> 0 when in u appears. (Hint: Use the properties of logarithms.) x10 Substitute for In x und du for dx in the integral Inx -dx= Integrale with...
4. Consider the semi-infinite string problem given by Utt = cʻuza, 0<x< 0,> 0 u(x,0) = f(x), 0<x< ~ ut(2,0) = g(2), 0 < x < 0 u(0,t) = 0, t> 0 Suppose that c=1, f(0) = (x - 1) - h(2 – 3) and g(C) = 0. (a) Write out the appropriate semi-infinite d'Alembert's solution for this problem and simplify. (b) Plot the solution surface and enough time snapshots to demostrate the dynam- ics of the solution.
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