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Fiesta28 [93]
2 years ago
8

PLZ HELP ME ASAP NO LINKS OR ABSURD ANSWERS

Mathematics
1 answer:
marusya05 [52]2 years ago
3 0

Answer:

sorry,dont know......

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Complete Question

The complete question is shown on the first uploaded

Answer:

y_1 is not a solution of the differential equation

 y_2 is not a solution of the differential equation

y_3 is not a solution of the differential equation

Step-by-step explanation:

The differential equation given is y'' + y' = cos2x

Let consider the first equation to substitute

y_1  = cosx  +sinx

y_1'  = -sinx  +cosx

y_1''  = -cosx -sinx

So

y_1'' - y_1'  = -cosx -sinx -sinx  +cosx

y_1'' + y_1'  = -2sinx

So

-2sinx \ne  cos2x

This means that y_1 is not a solution of the differential equation

Let consider the second equation to substitute

y_2 =  cos2x

y_2' =  -2sin2x

y_2'' =  -4cos2x

So

y_2'' + y_2'  = -4cos2x-2sin2x

So

-4cos2x-2sin2x \ne  cos2x

This means that y_2 is not a solution of the differential equation

Let consider the third equation to substitute

y_3 =  sin 2x

   y_3' =  2cos 2x

    y_3'' =  -4sin2x

So

y_3'' + y_3'  = -4sin2x  - 2cos2x

So

-4sin2x  - 2cos2x \ne  cos2x

This means  that  y_3 is not a solution of the differential equation

6 0
3 years ago
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