Solve the following IVP's1. y ′ = 1 − y , y ( 0 ) = 1

Question

Solve the following IVP&#039;s1.       y    ′    =  1  −  y  ,  y  (  0  )  =  1

Leon Webster · Accepted Answer

y&#039;=1-y, y(0)=1  ⇒            d      y              d      x        =  1  −  y  ⇒            d      y              1      −      y        =  d  x integrate both sides  ⇒  ∫      1          1      −      y        d  y  =  ∫  1  d  x  ⇒  1  −  y  =  u-dy=dudy =-du  ⇒  ∫            −      1        u    d  u  =  ∫  1  d  x  ⇒  −  ln  ⁡  (  1  −  y  )  =  x  +  c  ⇒  ln  ⁡  (  1  −  y      )          −      1        =  x  +  c  ⇒  ln  ⁡  (      1          1      −      y        )  =  x  +  c  ⇒      1          1      −      y        =      e          x      +      c        =      e          x            e          c        =  A  .      e          x       here   A  =      e          c       constant  y  ∗  A  .      e          x        =  A  .      e          x      −      1        y  (  x  )  =  1  −      1          A      .              e                  x                      =  1  +      C    ′        e          −      x       here C&#039;=-1/a constant

Solve the following IVP's 1. y'=1-y,y(0)=1

Answered question

Answer & Explanation

New Questions in Calculus 1