Verify that each given function is a solution of the differential equation.y"+2y'-3y=0; y sub one ( t ) = e − 3 t , y s u b 2 ( t ) = e t

Question

Verify that each given function is a solution of the differential equation.y&quot;+2y&#039;-3y=0;   y sub one   (  t  )  =      e          −      3      t        ,     y     s  u  b     2  (  t  )  =      e          t

Adelyn Mercado · Accepted Answer

given       y          1        (  t  )  =      e          −      3      t      differentiate       y          1        (  t  ) with respect to t, we have      y          1        ′    (  t  )  =  −  3      e          −      3      t      now       y          1        ″    (  t  )  =  9      e          −      3      t      put       y          1       and its derivatives in y&#039;&#039;+2y&#039;-3y, we get   0  (  9      e          −      3      t        −  6      e          −      3      t        −  3      e          −      3      t        =  0  )hence       y          1        (  t  ) is a solution to given DE y&#039;&#039;+2y&#039;-3y=0consider       y          2        (  t  )  =      e          t      differentiate       y          2        (  t  ) with respect to t, we have      y          2        ′    (  t  )  =      e          t      , now       y          2        ″    (  t  )  =      e          t      put       y          2       and its derivatives in y&#039;&#039;+2y&#039;-3y, we get   0  (      e          t        +  2      e          t        −  3      e          t        =  0  )this shows       y          2        (  t  ) is a solution to the DE y&#039;&#039;+2y&#039;-3y=0

Verify that each given function is a solution of the differential equation. y"+2y'-3y=0; y sub one (t)=e^(-3t), y sub2(t)=e^t

Answered question

Answer & Explanation

New Questions in Calculus 2