what's the solution of the differential equation y ′ = ( 2 x − y + 1 ) + 2

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what&#039;s the solution of the differential equation        y    ′    =      (    2    x    −    y    +    1    )    +  2

ce1ret3i · Accepted Answer

y    ′    =      (    2    x    −    y    +    1    )    +  2Put   (  2  x  −  y  +  1  )  +  2  =  t  2  −            d      y              d      x        =            d      t              d      x                  d      y              d      x        =  2  −            d      t              d      x      Now   (  1  )  →           2  −            d      t              d      x        =      2    x    −    y    +    1    +  2  −            d      t              d      x        =      t    →            d      t              t        =  −  d  xIntegrate on both sides  ∫      t          −              1        2              d  t  =  −  ∫  d  x        2                  t                  1          2                      =  −  x  +  c    ⇒  2      2    x    −    y    +  1  =  −  x  +  c    ⇒  2      2    x    −    y    +  1  +  x  =  c

Whats the solution of the diferential equation y'=sqrt(2×-y+1)+2

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