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In each of the Exercises 1 to 10 vrify t...

In each of the Exercises 1 to 10 vrify that the given functions(explicit or implicit) is a solution of the corresponding differential equation :
1. `y = e^(x) + 1 : y" - y' = 0`

Answer

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For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation. (i) xy = ae^(x) + be^(-x) + x^(2) : x (d^(2)y)/(dx^(2)) + 2(dy)/(dx) - xy + x^(2) - 2 = 0 (ii) y = e^(x)(a cos x + b sin x) : (d^(2)y)/(dx^(2))- 2(dy)/(dx) + 2y = 0 (iii) y = x sin 3x : (d^(2)y)/(dx^(2)) + 9y - 6 cos 3x = 0 (iv) x^(2) = 2y^(2) log y : (x^(2) + y^(2)(dy)/(dx) - xy = 0

Find order and degree of given differential equation y' + y = e^(x)

Knowledge Check

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

    A
    `e^(x) _ e^(-y) = C`
    B
    `e^(x) + e^(y) = C`
    C
    `e^(-x) + e^(y) = C`
    D
    `e^(-x) + e^(-y) = C`

  • The general solution of the differential equation (y dx - x dy)/(y ) = 0 is

    A
    `xy = C`
    B
    `x = Cy^(2)`
    C
    `y = Cx`
    D
    `y = Cx^(2)`

  • The general solution of the differential equation e^(x) dy + (y e^(x) + 2x)dx = 0 is

    A
    `x e^(y) + x^(2) = C`
    B
    `x e^(y) + y^(2) = C`
    C
    `y e^(x) + x^(2) = C`
    D
    `y e^(y) + x^(2) = C`

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    Find a particular solution of the differential equation (x + 1)(dy)/(dx) = 2e^(-y) - 1 , given that y = 0 when x = 0.

    Find the general solution of the differential equation y dx - (x + 2y^(2))dy = 0 .

    Verify that the function y = e^(-3x) is a solution of the differential equation (d^(2)y)/(dx^(2)) + (dy)/(dx) - 6y = 0

    Function y=e^(-3x) is solution of differential equation …..

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