(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...
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...