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STATEMENT-1 : To find complete solution ...

STATEMENT-1 : To find complete solution of a second order differential equation we need two different conditions.
and
STATEMENT-2 : An `n^(th)` order differential equation has n independent parameters.

A

Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is true, Statement-2 is true, Statement-2 is NOT a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • The second order differential equation is

    A
    `(y')^(2) = y^(2) - x`
    B
    y'y'' + y = sin x
    C
    `y''' + y'' + y = 0`
    D
    y' = y

  • Solution of the differential equation (dy)/(dx)+ytanx=x^(n)cosx is

    A
    `(n+1)y-x^(n-1)cosx=c(n+1)cosx`
    B
    `(n+1)y+x^(n-1)cosx=c(n+1)cosx`
    C
    `(n+1)y-x^(n-1)cosx=c(n+1)cosx`
    D
    `(n+1)y+x^(n-1)cosx=c(n+1)cosx`

  • STATEMENT-1 : If m and n are respectively order and degree of differential equation , then m and n are mutually independent. STATEMENT-2 : If general solution of a differential equation contains two arbitrary constants, then its order is 2. STATEMENT-3 : The order and degree of differential equation sqrt(1+((dy)/(dx))^(2)) = (x(d^(2)y)/(dx^(2)))^(1//3) are 2 and 2 respectively.

    A
    T F T
    B
    T T T
    C
    F F F
    D
    F F T

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    The order of the differential equation y'' + y^2+e^y'=0 is

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    The general solution of a differential equation is y= ae ^(bx+ c) where are arbitrary constants. The order the differential equation is :

    STATEMENT-1 : Solution of the differential equation xdy-y dx = y dy is ye^(x//y) = c . and STATEMENT-2 : Given differential equation can be re-written as d((x)/(y)) = -(dy)/(y) .

    STATEMENT-1 : The differential equation of all circles in a plane can be of order 3. and STATEMENT-2 : General equation of a circle in plane has three independent constant parameters

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