5. Usa the substituti on U(X, 1) = X(x) 7(1) and saparation of varlables to solve the partial differential aquation U11 = ; No boundary conditions are given. Take the separation constant as -a. Use the same mathods used to datermina the ganeral solution to the heat equation as demonstrated in your notes and determine

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Chapter2: Second-order Linear Odes
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Engineering Maths 3

5. Use tha substitution UX, t) = X(x) T(t) and saparation of variables to solve the partial differantial
equation
U11 = Ux
No boundary conditions ara given. Take the separation constant as -u. Usa the sama mathods used
to datermina the ganeral solution to the heat equation as demonstrated in your notes and determine
the most ganeral solution in terms of .
Transcribed Image Text:5. Use tha substitution UX, t) = X(x) T(t) and saparation of variables to solve the partial differantial equation U11 = Ux No boundary conditions ara given. Take the separation constant as -u. Usa the sama mathods used to datermina the ganeral solution to the heat equation as demonstrated in your notes and determine the most ganeral solution in terms of .
6. A LRC circ uit b alow is used to modiry an input voltage V; = @sin(@ t) + 2@ cos(@t) . For
this
application, R = 2 2, L = 2 H and C = F.Your dirrerential equ ation must be in terms or
20
charge q. You must use the complimantary and particular solution mathod as shown in your notes to
generate the genaral solution. No othar mathod will be acceptad. Use two decimal point accuracy. You
are givan that -2o² + 20N = 2w and -2M0² + 20M = 2w, which you m ust use to simpliry
your particular solution when you aquate coerricients.
HH
V.
V.
ko - L, sin(cst)
Vs
Transcribed Image Text:6. A LRC circ uit b alow is used to modiry an input voltage V; = @sin(@ t) + 2@ cos(@t) . For this application, R = 2 2, L = 2 H and C = F.Your dirrerential equ ation must be in terms or 20 charge q. You must use the complimantary and particular solution mathod as shown in your notes to generate the genaral solution. No othar mathod will be acceptad. Use two decimal point accuracy. You are givan that -2o² + 20N = 2w and -2M0² + 20M = 2w, which you m ust use to simpliry your particular solution when you aquate coerricients. HH V. V. ko - L, sin(cst) Vs
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