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AP EAMCET2001MathematicsDifferential Equations

The solution of d y d x +y=e^x is

Options

  1. A2 y=e^ 2 x +C
  2. B2 y e^x=e^x+C
  3. C2 y e^x=e^ 2 x +C
  4. D2 y e^ 2 x =2 e^x+C

Correct answer

C. 2 y e^x=e^ 2 x +C

Step-by-step solution

We have, d y d x +y=e^x On comparing with d y d x +P y=Q Here, P=1 and Q=e^x Now, IF =e^ 1 d x =e^x Complete solution is array rlrl & y e^x & = e^x e^x d x+C^ & y e^x & = e^ 2 x 2 +C^ & & y y e^x & =e^ 2 x +C array [ 2 C^ =C ]

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