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Question

 Given the differential equation dy/dx=-x/y^2 find the particular solution, y=f(x) , with the initial condition f(−6) = −3 .

Answer 1

Separate the variables:

y²dy=-xdx,

Integrate both sides:

y³/3=-x²/2+C.

Plug in y=-3, x=-6:

-9=-18+C, C=9, y³/3=-x²/2+9.

This can be written:

3x²+2y³-54=0.