One of the following is a general solution of the homogeneous differential equation y" + 7y' + 12y = 0 -3z ae + be 42 y = ae? + be ae 3z + be1z y = ae? + be 4z and one of the following is a solution to the nonhomogeneous equation y" + 7y + 12y = -40e y = -8e y = -2e y = -4e 6e By superposition, the general solution of the equation y" + 7y + 12y = -40e is Find the solution with y(0) = 2 y' (0) = 7 Being the highly trained differential equations fighting machine that I am, I checked the Wronskian (using the solutions to the homogeneous equation without the coefficients a and b) for good measure, and found it to be The fundamental theorem tells me that that this is the unique solution to the IVP on the interval

One of the following is a general solution of the homogeneous differential equation y" + 7y' + 12y = 0 -3z ae + be 42 y = ae? + be ae 3z + be1z y = ae? + be 4z and one of the following is a solution to the nonhomogeneous equation y" + 7y + 12y = -40e y = -8e y = -2e y = -4e 6e By superposition, the general solution of the equation y" + 7y + 12y = -40e is Find the solution with y(0) = 2 y' (0) = 7 Being the highly trained differential equations fighting machine that I am, I checked the Wronskian (using the solutions to the homogeneous equation without the coefficients a and b) for good measure, and found it to be The fundamental theorem tells me that that this is the unique solution to the IVP on the interval

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

One of the following is a general solution of the homogeneous differential equation y" + 7y' + 12y = 0
3z
ae
+ be 4z
y = ae" + be 1
ae 3z + be1z
y = ae? + be 4z
and one of the following is a solution to the nonhomogeneous equation y" + 7y + 12y = -40e
y = -8e
y = -2e
y = -4e
6e
By superposition, the general solution of the equation y" + 7y' + 12y = -40e is
Find the solution with
y(0) = 2
y' (0) = 7
Being the highly trained differential equations fighting machine that I am, I checked the Wronskian (using the solutions to the homogeneous
equation without the coefficients a and b) for good measure, and found it to be
The fundamental theorem tells
me that that this is the unique solution to the IVP on the interval

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