`dy/dx = 3x^2/y^2` Find the general solution of the differential equation

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`(dy)/dx = 3x^2/y^2`

This differential equation is separable since it can be rewritten in the form

`N(y)dy = M(x) dx`

So separating the variables, the equation becomes

`y^2dy = 3x^2dx`

Taking the integral of both sides, the equation becomes

`int y^2dy = int3x^2dx`

`y^3/3 + C_1 = 3*x^3/3 + C_2`

`y^3/3 + C_1 = x^3 + C_2`

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

`y^3/3 = x^3 + C`

 

Therefore, the general solution of the given `y^3/3 = x^3 + C` .

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