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For example I have the equation

y'=-2y^2

where a solution for it is:

y(t)=3/(6t-11)

with an initial value of:

y(2) = 3

in my TI Nspire I put in something such as:

y1'=−2*y1^(2)

but since I know y(2)=3 what do I do? exactly? Am I doing this right?

I also have another equation where:

y'+4y=cos(t)

a known solution of

y(t) = 4/17cos(t)+1/17sin(t)+Ce^-4t

and initial known value of:

y(0) = -1

should I solve this in terms of y' to plot it or what exactly?