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Show that the differential equation y^(3...

Show that the differential equation `y^(3)dy-(x+y^(2))dx=0` can be reduced to a homogenous equation.

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To show that the differential equation \( y^3 dy - (x + y^2) dx = 0 \) can be reduced to a homogeneous equation, we will follow these steps: ### Step 1: Rewrite the given equation We start with the given differential equation: \[ y^3 dy - (x + y^2) dx = 0 \] We can rearrange this into the form: ...
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