creative_22 :)
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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) |t|<infinity
Hint: from the identity cosh^2(t)-sinh^2(t)=1.
I tried changing sech and tanh into terms of sinh and cosh. Then I solved for t in terms of x and got t=cosh^(-1) (2/(x-3)) Replacing this back into the y equation for t I get something that is a lot more complicated. Any advice on another direction that I can go with this problem? Or a way to make it easier?
Now, I have: Let phi1(x) be a solution of the ODE y''(x)+y'(x)p(x)+y(x)q(x)=0 where p and q are contained in C(I). Verify that phi2(x) = phi1(x)* integral((e^-integral(p(x)dx))/phi1(x)^2 dx)
I tried taking the first and second derivative of phi2 and repalcing that in for y'',y',y respectively, however, I am a little stuck and am looking for advice on another way to solve this problem or a way to fix the way I am trying to solve this problem.
Thanks.
x=3+2sech(t), y=4-3tanh(t) |t|<infinity
Hint: from the identity cosh^2(t)-sinh^2(t)=1.
I tried changing sech and tanh into terms of sinh and cosh. Then I solved for t in terms of x and got t=cosh^(-1) (2/(x-3)) Replacing this back into the y equation for t I get something that is a lot more complicated. Any advice on another direction that I can go with this problem? Or a way to make it easier?
Now, I have: Let phi1(x) be a solution of the ODE y''(x)+y'(x)p(x)+y(x)q(x)=0 where p and q are contained in C(I). Verify that phi2(x) = phi1(x)* integral((e^-integral(p(x)dx))/phi1(x)^2 dx)
I tried taking the first and second derivative of phi2 and repalcing that in for y'',y',y respectively, however, I am a little stuck and am looking for advice on another way to solve this problem or a way to fix the way I am trying to solve this problem.
Thanks.