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For the first problem, I have: sketch the graph of the curve described by the point P(x,y) as the parameter t varies over the domain given. Also, find a Cartesian equation of the curve. Describe precisely how the graph is traced out as the parameter t varies. x=3+2sech(t), y=4-3tanh(t)...

The question is: Show that if lambda denotes a positive constant, and b is any real number, then any solution, say phi, of the ODE y'(x)+y(x)=be^-lambdax, has the property that phi->0 as x->+infinity. Comment: Be sure to treat all possible cases. To start, find the general solution of the given...