Solve the following differential equation: dy dx -y x = 2x^ 2 - Vidyadip

Question

Solve the following differential equation:

$\frac{dy}{dx} -\frac{y}{x} = 2x^{2}$

✓

Answer

Integrating factor $= e^{-\int\frac{dx}{x}}$

$= e^{-\int\frac{- logx}{}} = \frac{1}{x} $

The solution of different equation is

$ y^\frac{1} {x} = {\int\frac{2x^{2}}{x}} dx + c$

$y^{{}{}} \frac{1}{x} = x^{2} + c$ or

$y = x^{3} + cx$

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