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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(1+x^2)` `y'=(xy)/(1+x^2)`
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Solution
We have,
`y'=(xy)/(1+x^2) .......... (1)`
Now,
`y=sqrt(1+x^2)`
`rArr y'=x/(sqrt(1+x^2))`
Putting the above value in (1), we get
`"LHS" =x/(sqrt(1+x^2))`
`=x/(sqrt(1+x^2))xxsqrt(1+x^2)/sqrt(1+x^2)`
`=(xy)/(1+x^2)="RHS"`
Thus, `y=sqrt(1+x^2)` is the solution of the given differential equation.
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