Q5. (a) Find the value of lambda, for which the following differential equation will be an exact DE:(xy^2+2*lambda*x^2y)dx+(x+y)x^2dy=0(b) Find it’s general solution once you find a value of lambda in (a).(c) Use the inverse operator method to solve the following non-homogeneous ODE:y''+2y'+4y=e^2x*cosx Q5. (a) Find the value of 2, for which the following differential equation will be an exact DE:(xy² +22x²y)dx +(x+ y)x²dy = 0(b) Find it's general solution once you find a value of 2 in (a).(c) Use the inverse operator method to solve the following non-homogeneous ODE:y" + 2y'+ 4y = e2*cosx

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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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Q5. (a) Find the value of lambda, for which the following differential equation will be an exact DE:

(xy^2+2*lambda*x^2y)dx+(x+y)x^2dy=0
(b) Find it’s general solution once you find a value of lambda in (a).
(c) Use the inverse operator method to solve the following non-homogeneous ODE:

y''+2y'+4y=e^2x*cosx

Q5. (a) Find the value of 2, for which the following differential equation will be an exact DE:
(xy² +22x²y)dx +(x+ y)x²dy = 0
(b) Find it's general solution once you find a value of 2 in (a).
(c) Use the inverse operator method to solve the following non-homogeneous ODE:
y" + 2y'+ 4y = e2*cosx

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