1. у^2 =2 ху2. y^2=2xy3. dy+3ydx=0

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To solve these equations, we can start with the first equation:

Rearranging the equation:

у^2 - 2xу = 0

Factor out a у:

у(у - 2x) = 0

So, the solutions are у = 0 and у = 2x.

Moving on to the second equation:

Rearranging the equation:

y^2 - 2xy = 0

Factor out a y:

y(y - 2x) = 0

So, the solutions are y = 0 and y = 2x.

Finally, let's solve the third equation:

Separating variables:

dy = -3ydx

Integrating both sides:

∫(1/y) dy = ∫-3 dx

ln|y| = -3x + C

Solving for y:

y = e^(-3x + C)

Since C is the constant, we can rewrite this as:

y = ke^(-3x)

where k is the constant of integration.

These are the solutions to the given equations.