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"+2y + 5y = 6 sin 2r +7 cos 2r

"+2y + 5y = 6 sin 2r +7 cos 2r

Advanced Engineering Mathematics
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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2. Find the general solution of the differential equation (a) y" + 2y' + 5y = 6 sin 2r + 7 cos 2r (using method of undetermined coefficients) (b) y" + y = (using method of variation of parameter) 1+ sin r
Transcribed Image Text:2. Find the general solution of the differential equation (a) y" + 2y' + 5y = 6 sin 2r + 7 cos 2r (using method of undetermined coefficients) (b) y" + y = (using method of variation of parameter) 1+ sin r
Expert Solution
Step 1

Given that y''+2y'+5y=6sin2x+7cos2x

The objective is to solve the equation,

Now let's consider homogenous equation y''+2y'+5y=0,

Take m=ddx

Then the equation become like

m2+2m+5=0

If the equation is of the form ax2+bx+c=0 then the roots are x=-b±b2-4ac2a.

The roots for m2+2m+5=0 is,

m=-2±4-202=-2±4i2=-1±2i

Hence the solution is y=e-xc1cos2x+c2sin2x.

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