What are the common things in using the variation of parameter methods to solve 1st-order and 2nd-order linear inhomogeneous ODES? Select one or more: O The coefficients in front of the dependent variable and its derivatives need to be constant. O We need to solve the homogenous O O We need to vary the arbitrary constant(s) in the general solution to the homogenous ODE to an unknown function of y. O We need to vary the arbitrary constant(s) in the general solution to the homogenous ODE to an unknown function of x. O We need to differentiate the assumed solution up to the order of the ODE, i.e. getting the expression of y' (or y' and y"), and put it (them) back to the original ODE. is ODE first.

What are the common things in using the variation of parameter methods to solve 1st-order and 2nd-order linear inhomogeneous ODES? Select one or more: O The coefficients in front of the dependent variable and its derivatives need to be constant. O We need to solve the homogenous O O We need to vary the arbitrary constant(s) in the general solution to the homogenous ODE to an unknown function of y. O We need to vary the arbitrary constant(s) in the general solution to the homogenous ODE to an unknown function of x. O We need to differentiate the assumed solution up to the order of the ODE, i.e. getting the expression of y' (or y' and y"), and put it (them) back to the original ODE. is ODE first.

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

What are the common things in using the variation of parameter methods to solve 1st-order and 2nd-order linear inhomogeneous ODES?
Select one or more:
O The coefficients in front of the dependent variable and its derivatives need to be constant.
O We need to solve the homogenous ODE first.
We need to vary the arbitrary constant(s) in the general solution to the homogenous ODE to an unknown function of y.
We need to vary the arbitrary constant(s) in the general solution to the homogenous ODE to an unknown function of x.
O We need to differentiate the assumed solution up to the order of the ODE, i.e. getting the expression of y' (or y' and y"), and put it
(them) back to the original ODE.

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