In Exercises 10-13, use the complex method, as in Exam- ple 5.12, to find a particular solution for the differential equa- tion. 12. y" +7y' + 6y = 3 sin 2t

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Q: (sim (6)) 45. y - (1 + uan ()) 6. y = ¿(1 + cos (7)" 43. y sin (cos (2r - 5)) Eises 44. y= cos (5…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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Q: Q.1 In the study offrost penetration in highway engineering the temperature T at time t hours and…

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Q: العنوان solve b sin ² (3x) cos² (5x) dx 2 8 tan³x dx >

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Q: 9.) y(4) + 2y" +y = x² sinx

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A: Identities of hyperbolic trigonometric function  cosh2z-sinh2z=1tanhz=sinhzcoshz1coshz=sechz

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Q: Solve rue I.v.P. ý + 3y'-s y = y co1=2 yco)=-3

A: Given,y(0)=2 and y'(0)=-3y''+3y'-5y=0    Integrating both sides y'+3y-5=C1...............(1)on again…