How do you solve dy/dt = t/(y+1)? Don't you get 2 y's on one side of the equation, so how would you solve for y(t)?
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1. multiply both sides by dt, you get dy = (t dt) /(y+1)
2. multiply both sides by (y+1), you get (y+1) dy = t dt
3. integrate both sides, you get (y^2)/2 + y = (t^2)/2, which is the implicit form of the solution