`dy/dx = x/y` Find the general solution of the differential equation

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`(dy)/dx = x/y`

This differential equation is separable since it can be re-written in the form

  • `N(y)dy = M(x)dx`

So separating the variables, the equation becomes

`ydy = xdx`

Integrating both sides, it result to

`int y dy = int x dx`

`y^2/2 + C_1 = x^2/2 + C_2`

Isolating the y, it becomes

`y^2/2 =x^2/2+C_2-C_1`

`y^2=x^2 + 2C_2 - 2C_1`

`y=+-sqrt(x^2+2C_2-2C_1)`

Since C2 and C1 represents any number, it can be expressed as a single constant C.

`y = +-sqrt(x^2+C)`

 

Therefore, the general solution of the given differential equation is `y = +-sqrt(x^2+C)` .

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