Solve the following differential equation: `(1+x^2)dy=x y\ dx`

Explanation

`(1+x^{2}) d y=x y d x`


`Rightarrow frac{1}{y} d y=frac{x}{1+x^{2}} d x`


integrate both sides


`int frac{1}{y} d y=int frac{x}{1+x^{2}} d x`


Assume `1+x^{2}=t,`


Put value in the equation, we get


`2 x d x=d t `


` int frac{1}{y} d y=frac{1}{2} int frac{1}{t} d t `


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