- #1
ProPatto16
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Homework Statement
seperate and solve using partial fractions
dx/dt=9-4x2, x(0)=0
The Attempt at a Solution
rearranging gives dx/(9-4x2) = dt
factorising denominator in preperation for partial fractions becomes
dx/(3-2x)(3+2x) then A/(3-2x) + B/(3+2x) dx
so A(3+2x)+ B(3-2x) = 1
therefore 3A+3B=1 and 2Ax-2Bx=0 therefore A+B=1/3 and A-B=0 therefore A=1/6 and B=1/6
so integral becomes
(1/6)/(3-2x) + (1/6)/(3+2x) dx = 1/6*-1/2ln|3-2x| + 1/6*1/2ln|3+2x|
and RHS is just t+C
with x(0)=0 then C = 0
the Answer is given as x(t)=[3(1-e-12t)]/[2(1+e-12t)]
but i can't seem to manipulate my answer to get there...