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find the order and degree of D.E : (1)...

find the order and degree of D.E : (1) ` ((d^(2)y)/(dx^(2) ))^2 + ((dy)/(dx))^(3) = e^(x)` (2) ` sqrt(1 + 1/((dy)/(dx))^(2))= ((d^(2)y)/(dx^(2)))^(3/2)` (3) ` e^((dy)/(dx))+ (dy)/(dx) =x`

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(1) The given D.E. `((d^(2)y)/(dx^(2))^(2)) + ((dy)/(dx))^(3)) = e^(x)`
The D.E. has highest order derivative ` (d^(2)y)/(dx^(2))` with power 2.
The given D.E. of order 2 and degree 2.
(2) The given D.E. is `sqrt(1+1/(((dy)/dx)^(2)))=((d^(2)y)/(dx^(2)))^(3/2)` on squaring both sides, we get ,
`1/((dy/(dx))^(2))=((d^(2)y)/(dx^(2)))^(3)`
` (dy/(dx))^(2) + 1= ((d^(2)y)/(dx^(2)))^(3). ((dy)/(dx))^(2)`
This D.E. has highest order derivative ` (d^(2)y)/(dx^(2))` with power 3.
order =2 and degree = 3.
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Knowledge Check

  • The order and degree of D.E. (d^(2)y)/(dx^(2))=root3(1+((dy)/(dx))^(2)) are

    A
    3, 2
    B
    3, 1
    C
    2, 3
    D
    2, 2

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