a) Transform the following Cauchy Euler equationto a differential with constant coefficients by using the substitution x = e' and hence solve it x’y" + xy' + y = 3+ h x. b) Solve the non-homogeneous higher order differential equation y" + y =x' cos x. a) Use the method of Superposition Approach and the variation of parameter to solve the differential equation 3y" – 6y' + 30.y= sin x + e* tan 3x . b) Use Laplace Transform to solve the initial value problem y" – 4y' + 4y =r'e" y(0) = 0,y'(0) = 0 a) State the Convolution theorem. Find the Inverse Laplace Transform - +1) b) By using the Laplace transform show that L costdt 25 27 where cos a) Evaluate L{F(t)}where F(t) = t> 2л where t<

a) Transform the following Cauchy Euler equationto a differential with constant coefficients by using the substitution x = e' and hence solve it x’y" + xy' + y = 3+ h x. b) Solve the non-homogeneous higher order differential equation y" + y =x' cos x. a) Use the method of Superposition Approach and the variation of parameter to solve the differential equation 3y" – 6y' + 30.y= sin x + e* tan 3x . b) Use Laplace Transform to solve the initial value problem y" – 4y' + 4y =r'e" y(0) = 0,y'(0) = 0 a) State the Convolution theorem. Find the Inverse Laplace Transform - +1) b) By using the Laplace transform show that L costdt 25 27 where cos a) Evaluate L{F(t)}where F(t) = t> 2л where t<

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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Concept explainers

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

a) Transform the following Cauchy Euler equationto a differential with constant coefficients by using
the substitution x = e' and hence solve it x’y" + xy' + y = 3+ h x.
b) Solve the non-homogeneous higher order differential equation y" + y =x' cos x.
a) Use the method of Superposition Approach and the variation of parameter to solve the differential
equation 3y" – 6y' + 30.y= sin x + e* tan 3x .
b) Use Laplace Transform to solve the initial value problem y" – 4y' + 4y =r'e" y(0) = 0,y'(0) = 0
a) State the Convolution theorem. Find the Inverse Laplace Transform -
+1)
b) By using the Laplace transform show that L
costdt
25
27
where
cos
a) Evaluate L{F(t)}where F(t) =
t>
2л
where t<

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