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Question
In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-
`y=sqrt(a^2-x^2)` `x+y(dy/dx)=0`
Solution
We have,
`x+y(dy)/(dx)=0 .............(1)`
Now,
`y=sqrt(a^2-x^2)`
`rArry'=(-x)/(sqrt(a^2-x^2))`
Putting the above value in (1), we get
`"LHS" =x+y((-x)/(sqrt(a^2-x^2)))`
`=x+sqrt(a^2-x^2)xx(-x)/(sqrt(a^2-x^2))`
`=x-x=0=" RHS"`
Thus, `y=sqrt(a^2-x^2)` is the solution of the given differential equation.
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