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The first step is to differentiate the substitution.Because u=2+ln(t) we can differentiate to get du=(1/t) dt which can be rearranged to dt=t du.Once we have this we can start on the actual expression. We...

y=e^2x-9. When x=0 y=a.a=e²⁽⁰⁾-9a=1-9=-8.
When x=b y=0.0=e^2(b)-99=e^2bln(9)=ln(e^2b)ln(9)=2b(1/2)ln(9)=bln(9^(1/2))=bb=ln3

The equation given needs to be transformed into a more familiar equation of a circle which we know the properties of and are therefore able to find its centre. Do you know what type of equation im speakin...

First convert y into a suitably form.cos(2x) = 1 - 2cos²(x)cos²x = (1-cos(2x))/2
integral of y = integral of (1-cos(2x))/2 = (1/2)*(x-(1/2)sin(2x)) + C = x/2 - sin(2x)...

dy/dx = (2x-y²)/(2xy)Stationary points: (1, root(2)) , (1, -root (2))