Find the solution of the given initial value problem. y" + 2y' + 2y = cost + 8(1 - 5); y(0) = 5, y' (0) = 4 y) = - taz()ef"cost + cos( Se" +) + sine (9e + + sint( 9e- + 24 Un/2(1)e sint + sint 42 +...

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Extracted text: Find the solution of the given initial value problem. y" + 2y' + 2y = cost + 8(1 - 5); y(0) = 5, y' (0) = 4 y) = - taz()ef"cost + cos( Se" +) + sine (9e + + sint( 9e- + 24 Un/2(1)e sint + sint 42 + cost 5° y(t) = + 5 x) = - ta)et"cost + cos(+) + sine ( +) 24 - Uz/2(t)ez¯'cost + cost( 5 42 5 24 42 y(t) = Un/2(1)e¯† cost + cost + sint 5 re -e + 5 5 24 y(t) = un/2(t)e'sint + cost 5 + 5 42 + sint 5 + 5