Final answer to the problem
$y=\frac{C_1}{x^{2}}$
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Step-by-step Solution
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- Equazione differenziale separabile
- Equazione differenziale omogenea
- Prodotto di binomi con termine comune
- Metodo FOIL
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1
Group the terms of the equation
$x\cdot dy=-2y\cdot dx$
Learn how to solve equazioni differenziali problems step by step online.
$x\cdot dy=-2y\cdot dx$
Learn how to solve equazioni differenziali problems step by step online. 2ydx+xdy=0. Group the terms of the equation. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Apply the formula: b\cdot dy=a\cdot dx\to \int bdy=\int adx, where a=\frac{-2}{x}, b=\frac{1}{y}, dyb=dxa=\frac{1}{y}dy=\frac{-2}{x}dx, dyb=\frac{1}{y}dy and dxa=\frac{-2}{x}dx. Solve the integral \int\frac{1}{y}dy and replace the result in the differential equation.
Final answer to the problem
$y=\frac{C_1}{x^{2}}$
