Question

2 solve x² dy = y² + 1 dx​

Answer 1

Answer:

The answer is $\tan^{-1}y=-\frac{1}{x}+c$

Step-by-step explanation:

Given differential equation is

              $x^2dy=(y^2+1)dx$

Separate the variables        

                $\displaystyle \Rightarrow \frac{dy}{y^2+1}=\frac{dx}{x^2}$

Now integrate both sides

               $\Rightarrow \displaystyle \int\frac{dy}{1+y^2}=\int x^{-2}dx\\\Rightarrow \tan^{-1}}y=\frac{x^{-2+1}}{-2+1}+c\\\Rightarrow \tan^{-1}y=-\frac{1}{x}+c$

Answer 2

Answer:

hi and this example was you help