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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)

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

Knowledge Check

  • Which of the following differential equations has y = c_(1)e^(x) + c_(2)e^(-x) as the general solution?

    A
    `(d^(2)y)/(dx^(2)) + y = 0`
    B
    `(d^(2)y)/(dx^(2))-y = 0`
    C
    `(d^(2)y)/(dx^(2)) + 1 = 0`
    D
    `(d^(2)y)/(dx^(2))-1=0`

    • Similar Questions

    Explore conceptually related problems

    For each of the differential equations in Exercises 11 to 14, find a particular solution satisfying the given condition: 11. (x^(3) + x^(2) + x+ 1)(dy)/(dx) = 2x^(2) + x, y = 1 when x = 0.

    If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx) . x = sin t, y= cos 2t .

    For each of the differential equations given below, indicate its order and degree(if defined). (i) (d^(2)y)/(dx^(2))+ 5x((dy)/(dx))^(2) - 6y = log x (ii) ((dy)/(dx))^(3) - 4((dy)/(dx))^(2) + 7y = sin x (iii) (d^(4)y)/(dx^(4)) - sin ((d^(3)y)/(dx^(3)) = 0

    If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx) . x= 2at^(2), y= at^(4) .

    If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx) . x= a (cos theta+ theta sin theta), y= a (sin theta-theta cos theta) .

    If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx) . x= a(theta-sin theta), y= a (1+ cos theta) .

    If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx) . x= a(cos t+ log tan (t)/(2)), y= a sin t .

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