Recent content by potatocake

Then do I have to solve two different differential equations?

(x cos(y) + x2 +y ) dx = - (x + y2 - (x2)/2 sin y ) dy I integrated both sides 1/2x2cos(y) + 1/3 x3+xy = -xy - 1/3y3+x2cos(y) Then I get x3 + 6xy + y3 = 0 Am I doing the calculations correctly? Do I need to solve it in another way?

I suppose it will form Qn = 0.5Qn+1+0.5Qn-1 ...? then will the probability of terminating at 0 given that we start from 0 is Q0 = 1 and probability of terminating at 0 given that we start from N is QN = 0.5QN+1 + 0.5QN-1?? Then how would I solve the differential equation? Through...

Does that mean my general formula is wrong? Does that mean I have to get Pn(0) ?

I want to solve this using difference equation. So I set up the general equation to be Pi = 0.5 Pi+1 + 0.5 i-1 I changed it to euler's form pi = z 0.5z2-z+0.5 = 0 z = 1 since z is a repeated real root I set up general formula Pn = A(1)n+B(1)n then P0 = A = 1 PN = A+BN = 0 -> A= -BN...

I attempted to solve it $$ x = \frac {1}{4x} + 1 $$ $$⇒ x^2 -x -\frac{1}{4} = 0 $$ $$⇒ x = \frac{1±\sqrt2}{2} $$ However, I don't know the next step for the proof. Do I need a closed-form of xn+1or do I just need to set the limit of xn and use inequality to solve it? If I have to use...