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Let y(x) be a solution of the differenti...

Let `y(x)` be a solution of the differential equation `(1+e^(x))y^(')+ye^(x)=1`. If `y(0)=2`, then watch of the following statements is (are) true?

A

y(-4)=0

B

y(-2)=0

C

y(x) has a critical point in the interval (-1,0)

D

y(x) has no critical point in the interval (-1,0)

Text Solution

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The correct Answer is:
A, C, D
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Knowledge Check

  • The general solution of the differential equation (e^(x)+1)y dy=(y+1)e^(x)dx is

    A
    `(y+1)=k(e^(x)+1)`
    B
    `y+1=e^(x)+1+k`
    C
    `y=log{k(y+1)(e^(x)+1)}`
    D
    `y=log{(e^(x)+1)/(y+1)}+k`

  • The solution of the differential equation (dy)/(dx)=e^(x-y)+x^(2)e^(-y) is

    A
    `y=e^(x-y)-x^(2)e^(-y)+c`
    B
    `e^(y)-e^(x)=(x^(3))/3+c`
    C
    `e^(x)+e^(y)=(x^(3))/3+c`
    D
    `e^(x)-e^(y)=(x^(3))/3+c`

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