The general solution of the differential equation [tex]\frac{dy}{dx} = \frac{8x}{y}[/tex] using variable separable method is [tex]y^{2}= 8 x^{2} +C[/tex].
If it is possible to write a differential equation by the transportation of terms, in the form f(x) dx = g(y) dy where f(x) is the function of x and g(y) is the function of y, then we say that variables are separable.
The solution is given by:
[tex]\int\ {f(x)} \, dx = \int\ {g(y)} \, dy + c[/tex]
where c is the arbitrary constant.
[tex]\frac{dy}{dx} = \frac{8x}{y} \\\\y\, dy = 8x \,dx\\\\\int\ {y} \, dy = \int\ {8x} \, dx\\\\\frac{y^{2} }{2} = \frac{8x^{2} }{2} + C \\\\y^{2}= 8 x^{2} +C[/tex]
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