Q5. (a) Find the value of 2, for which the following differential equation will be an exact DE: (xy + 22x²y)dx+(x+ y)x°dy =0 (b) Find it's general solution once you find a value of à in (a). (c) Use the inverse operator method to solve the following non-homogeneous ODE: y" + 2y'+ 4y = e2* cosx

Q5. (a) Find the value of 2, for which the following differential equation will be an exact DE: (xy + 22x²y)dx+(x+ y)x°dy =0 (b) Find it's general solution once you find a value of à in (a). (c) Use the inverse operator method to solve the following non-homogeneous ODE: y" + 2y'+ 4y = e2* cosx

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.

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Q5. (a) Find the value of 1, for which the following differential equation will be an exact DE:
(xy +22x*y)dx+(x+y)x²dy=0
(b) Find it's general solution once you find a value of 1. in (a).
(c) Use the inverse operator method to solve the following non-homogeneous ODE:
y" + 2y' + 4y = e2x cosx

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