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For each of the differential equations g...

For each of the differential equations given inExercises 1 to 12, find the general solution :
1.`(dy)/(dx) + 2y = sin x`

Text Solution

Verified by Experts

The correct Answer is:
`y = (1)/(5)(2 sin x - cos x) + Ce^(-2x)`
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For each of the differential equations in Exercises 1 to 10, find the general solution: 1. (dy)/(dx) = (1 - cos x)/(1 + cos x)

Find the general solution of (dy)/(dx)=(2y)/(x) .

Knowledge Check

  • The solution of sin^(-1)((dy)/(dx)) = y + x is

    A
    `Tan (x+y) - sec(x + y) = x + c`
    B
    `Tan ((x+y)/(2)) = c`
    C
    `Tan(x+y) = x+c`
    D
    `Tan(x+y) - sec (x+y) = c`

  • The solution of the differential equation y dx - x dy = 0 is

    A
    `y^(2) = cx^(3)`
    B
    `y = cx^(2)`
    C
    `y = cx`
    D
    `y^(2) = cx`

  • The solution of the differential equation y dx + x dy = 0 is

    A
    `xy = c`
    B
    `x + y = c`
    C
    `x - y = c`
    D
    `x//y = c`

    • Similar Questions

    Explore conceptually related problems

    Find the general solution of : (dy)/(dx)=(2y)/(x)

    For each of the differential equations given in Exercises 13 to 15, find a particular solution satisfying the given condition: 13. (dy)/(dx) + 2 y tan x = sin x, y = 0 when x = (pi)/(3)

    For each of the differential equations in Exercises from 11 to 15, find the particular solution satisfying the given condition : 11. ( x + y) dy + ( x - y) dx = 0, y = 1 when x = 1

    Find the general solution of the differential equation (dy)/(dx) - y = cosx.

    Solution the differential equation (dy)/(dx) + 1 = e^(x+y) is

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