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State which of the following problems are under-determined (that is, having insufficient boundary conditions to determine all the arbitrary constants in the general solution) and which are fully-determined. In case of fully-determined problems state which are the boundary problems and which are initial-value problems (Do not attempt to solve the DES). a. x² = sint, x(0) <= a. d²x 1, dx b. 4x- +(2+²_1) - 4x²t=0, dt² dt d²x dx dx C. dx dt d. dt2 dt d³x dt3 4 = 2t², + x = dt d²x dx 2- + dt² dt x(0) = 4, dx dt x(1) = 0, - 4x = t² +t+1, dx dt -(1) = = 1. (1) = 0. x(0) = 1, x(2) = 0.

State which of the following problems are under-determined (that is, having insufficient boundary conditions to determine all the arbitrary constants in the general solution) and which are fully-determined. In case of fully-determined problems state which are the boundary problems and which are initial-value problems (Do not attempt to solve the DES). a. x² = sint, x(0) <= a. d²x 1, dx b. 4x- +(2+²_1) - 4x²t=0, dt² dt d²x dx dx C. dx dt d. dt2 dt d³x dt3 4 = 2t², + x = dt d²x dx 2- + dt² dt x(0) = 4, dx dt x(1) = 0, - 4x = t² +t+1, dx dt -(1) = = 1. (1) = 0. x(0) = 1, x(2) = 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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State which of the following problems are under-determined (that is, having insufficient boundary conditions to determine all the arbitrary constants in the general solution) and which are fully-determined. In case of fully-determined problems state which are the boundary problems and which are initial-value problems (Do not attempt to solve the DES). a. C. dx dt b. 4x- d. d²x dt² d²x dx dt² dt d³ x 4- dt3 = sint, x(0) = a. 1 dx x' dt +(2t². dx +x - dt d² x 2- dx dt² dt 2t², + - 4x²t=0, x(0) = 4, dx x(1) = 0, dt 4x = t² + t + 1, dx dt -(1): = 1. (1) = 0. x(0) = 1, x(2) = 0.
Transcribed Image Text:State which of the following problems are under-determined (that is, having insufficient boundary conditions to determine all the arbitrary constants in the general solution) and which are fully-determined. In case of fully-determined problems state which are the boundary problems and which are initial-value problems (Do not attempt to solve the DES). a. C. dx dt b. 4x- d. d²x dt² d²x dx dt² dt d³ x 4- dt3 = sint, x(0) = a. 1 dx x' dt +(2t². dx +x - dt d² x 2- dx dt² dt 2t², + - 4x²t=0, x(0) = 4, dx x(1) = 0, dt 4x = t² + t + 1, dx dt -(1): = 1. (1) = 0. x(0) = 1, x(2) = 0.
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