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)`

Answer 1

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.