Find the general solution of the following differential equation: dy/dx = x/(x^2 +1)

Question

Find the general solution of the following differential equation:

\(\frac{dy}{dx}\) = \(\frac{x}{(x^2+1)}\)

Answer 1

dy = \(\frac{x}{x^2+1}\)dx

Multiply and divide 2 in numerator and denominator of RHS,

y = \(\frac{1}2\).\((\frac{2x}{x^2+1}dx)\)

Integrating on both sides

y = \(\frac{1}2\).log (x² + 1) + c