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Solution of dydx−y=1,  y(0)=1  is given by

(A) xy=−ex

(B) xy=−e−x

(C) xy=−1

(D) y=2ex−1

0 2 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    3 months ago

    This is an Objective Type Questions as classified in NCERT Exemplar

    Sol:

    The  given  differential  equation  is                    dydx−y=1Here,  P=−1  and  Q=1So,  integrating  factor=e∫Pdx=e∫−1dx=e−xSo,  the  solution  is                y×I.F=∫Q×I.F.dx+c⇒            y×e−x=∫1.e−x.dx+c⇒               y.e−x=−e−x+cPut  x=0,  y=1⇒                1.e0=−e0+c⇒                       1=−1+c                ∴c=2So,  the  equation  is  y.e−x=−e−x+2⇒                          y=−1+2ex=2ex−1Hence,  the  correct  option  is  (d).

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