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Which of the following differential eq...

Which of the following differential equations has y = x as one of its particular solution?
(A) `(d^2y)/(dx^2)-x^2(dy)/(dx)+x y=x`
(B) `(d^2y)/(dx^2)+x(dy)/(dx)+x y=x`
(C) `(d^2y)/(dx^2)-x^2(dy)/(dx)+x y=0`
(D) `(d^2y)/(dx^2)+x(dy)/(dx)+x y=0 `

A

`(d^(2)y)/(dx^(2))-x^(2)(dy)/(dx)+xy=x`

B

`(d^(2)y)/(dx^(2))-x(dy)/(dx)+xy=x`

C

`(d^(2)y)/(dx^(2))-x^(2)(dy)/(dx)+xy=0`

D

`(d^(2)y)/(dx^(2))+x(dy)/(dx)+xy=0`

Text Solution

Verified by Experts

Given, `y=x`……`(1)`
Differntiate w.r.t.x, `(dy)/(dx)=1`……..`(2)`
Again, differentiate w.r.t.x, `(d^(2)y)/(dx^(2))=0`………`(3)`
Now put the value of `y` from equation `(1)`, value of `y'` from equaion `(2)` and value of `y''` in equation `(3)` in each differential equation. We find that only the differential equation given in option `(c )` satisfies.
`(d^(2)y)/(dx)-x^(2)(dy)/(dx)+xy=0-x^(2)*1+x*x`
`=-x^(2)+x^(2)=0`
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