Annette Sabin

2022-01-22

Solve the first-order differential equations:
$\left({x}^{2}+1\right)\frac{dy}{dx}=xy$

Ana Robertson

Expert

Solution:
$\left({x}^{2}+1\right)\frac{dy}{dx}=xy$

This is a separable linear first order differential which is of the form
$N\left(y\right)dy=M\left(x\right)dx$

Intagrating both sides
$\int \frac{1}{y}dy=\int \frac{x}{{x}^{2}+1}dx$
Let ${x}^{2}+1=u$

So,

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