Question

dy/dt = -t^3y^2-ty^2

dx/dt=(sin t)/(cos t+10)

dy/dx -3y/x =x^3cosx

Which differential method should be used for each equation?

Answer 1

I'd say

separation of variables, since you can write it as

dy/y^2 = -(t+t^3) dt

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next is just direct integration, since you already have dy/dt as a function of t.

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The last is of the form

y' + y p(x) = q(x)

so look for an integrating factor