Verify that given function is a solution of the differential equation.y""+4y"'+3y=t; y subone(t)=t/3, y sub two ( t ) = e − t + t / 3

Question

Verify that given function is a solution of the differential equation.y&quot;&quot;+4y&quot;&#039;+3y=t; y subone(t)=t/3, y sub two  (  t  )  =      e          −      t        +  t      /    3

Gauge Howard · Accepted Answer

y          1        (  t  )  =  t      /    3  ,      y          2        (  t  )  =      e          −      t        +  t      /    3.      y          1        =  t      /    3      y          1        ′    =  1      /    3      y          1        ″    =      y          1        ‴    =      y          1        ⁗    =  0      y          1        ⁗    +  4      y          1        ‴    +  3      y          1        =  0  +  0  +  t  =  t  .      y          2        =      e          −      t        +  t      /    3      y          2        ′    =  −      e          −      t        +  1      /    3      y          2        ″    =      y          2        ⁗    =      e          −      t            y          2        ‴    =  −      e          −      t        .      y          2        ⁗    +  4      y          2        ‴    +  3      y          2        =      e          −      t        −  4      e          −      t        +  3  (      e          −      t        +  t      /    3  )  =      e          −      t        −  4      e          −      t        +  3      e          −      t        +  t  =  t  .

Max Macias · Accepted Answer

y          (      4      )        +  4      y          (      3      )        +  3  y  =  t  ,      y          1        =  t      /    3  ,      y          2        =      e          −      t        +  t      /    3      y          1        ′    =      1    3    ,      y          1        ″    =      y          1              (      3      )        =      y          1              (      4      )        =  0  ⇒  0  +  4  (  0  )  +  3  (  t      /    3  )  =  tt=t Check.      y          2        ′    =  −      e          −      t        +  1      /    3.      y          2        ″    =      e          −      t        ,      y          2              (      3      )        =  −      e          −      t        ,      y          2              (      4      )        =      e          −      t        ⇒      e          −      t        +  4  (  −      e          −      t        )  +  3  (      e          −      t        +  t      /    3  )  =  t      e          −      t        −  4      e          −      t        +  3      e          −      t        +  t  =  tt=t Check.

Verify that given function is a solution of the differential equation. y""+4y"'+3y=t; y subone(t)=t/3, y sub two (t)=e^(-t)+t/3

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