I am studying for my final and this is one of the problems in out trial final, ive gone through it about 56 times and i can not for the life of me get it right.
the pic and question is attached
What i have is
dx/dt=2(3x/100)+(y/200)
dy/dt=(3x/100)(3y/200)
I solve the second equation for x
x=(dy/dt)(100/3)+(y/2) and that gives me x' as
x'=(d^2y/dt^2)(100/3)+(dy/dt)(1/2)
then i plug back into the equation and collect like terms and i get
(100/3)(d^2y/dt^2)+(dy/dt)(1/2)=2(3/100)[(dy/dt)(100/3)+(y/2)] +(y/200)
which simplifies to
(d^2y/dt^2)+(9/200)(dy/dt)+(3/10000)y=2
Then i find my two solutions for
(d^2y/dt^2)+(9/200)(dy/dt)+(3/10000)y=0
and this is were it all goes wrong...
Please help! Thank you
the pic and question is attached
What i have is
dx/dt=2(3x/100)+(y/200)
dy/dt=(3x/100)(3y/200)
I solve the second equation for x
x=(dy/dt)(100/3)+(y/2) and that gives me x' as
x'=(d^2y/dt^2)(100/3)+(dy/dt)(1/2)
then i plug back into the equation and collect like terms and i get
(100/3)(d^2y/dt^2)+(dy/dt)(1/2)=2(3/100)[(dy/dt)(100/3)+(y/2)] +(y/200)
which simplifies to
(d^2y/dt^2)+(9/200)(dy/dt)+(3/10000)y=2
Then i find my two solutions for
(d^2y/dt^2)+(9/200)(dy/dt)+(3/10000)y=0
and this is were it all goes wrong...
Please help! Thank you
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