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Chrome File Edit View History Bookmarks People Window Help 81% Wed Oct 21 9:53 PM EE G Scandals x Band of x WA http://abo x 2 Accuse x Sections x Did Ambr x LexisNeexi X History N x College G X Chegg St X Guid X c www.webassign.net/web/Student/Assignment-Responses/last?dep 12565783#Q9 ABI 9. 0/1 points I Previous Answers ZillDiffEQ8 4.6.005 Solve the differential equation by variation of parameters. y(x) Need Help? Read It Chat About It Submit Answer Save Progress Practice Another Version 10 -1 points ZillDiffEQ8 4.6.011

Solution

y = A sin x + B cos x + y_p
y = u cos x
y\' = u\' cos x - u sin x
y\'\' = u\'\' cos x - 2u\' sin x - u cos x
y\'\' + y\' = u\'\' cos x - 2u\' sin x = cos^2 x

u\'\' cos x - u\' 2 sin x = cos^2 x
integrate both sides

sinx x u\' = 1/2x+1/2six cos x
u\' = 1/2
u = 1/2 x
y_p = 1/2 x+1/2sinx cos x

y = A sin x + B cos x + 1/2 x +1/2 sin x cos x