Substitute 

, so that

![\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%5Cright%5D%3D-%5Cdfrac1%7Bx%5E2%7D%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%2B%5Cdfrac1x%5Cleft%28%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dz%5E2%7D%5Cright%29%3D%5Cdfrac1%7Bx%5E2%7D%5Cleft%28%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dz%5E2%7D-%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%5Cright%29)
Then the ODE becomes


which has the characteristic equation 

 with roots at 

. This means the characteristic solution for 

 is

and in terms of 

, this is

From the given initial conditions, we find


so the particular solution to the IVP is
 
 
        
        
        
$46 divided by 5 which equals $9.50
        
                    
             
        
        
        
Answer:
Part a) 
We need to find the equation of a straight line passing through two given points in slope-intercept form
Part b)
The information given; we are given two points where the line passes through; (0, -4) and (-2, 2)
Part c)
We shall first determine the slope of the line using the formula;
change in y/change in x. Next, we determine the value of the y-intercept using the general form of the equation of a straight line in slope-intercept form; y = mx+c
Part d)
The slope of the line is calculated as;
(2--4)/(-2-0) =6/-2 = -3
The equation of the line in slope-intercept form becomes;
y = -3x +c
We use the point (0, -4) to determine the value of c;
-4 = -3(0)+c
c = -4
Part e)
Final solution thus becomes;
y=-3x-4
 
        
             
        
        
        
Answer:
a) 0.122
b) 3.35 × 10⁻⁴
c) 0.1071
Step-by-step explanation:
 Here we have the Poisson process given by

Where:
λ = Rate = 4 bites/hour and 
t = Length of time that is 
Mean = λt
Where k = 6 fishes bites and t = 2 hours we have

b) The probability that he fails to catch any fishes during the first two hours is the probability t that he catches 0 fish as follows
 
(c) Here we have

For 1 fish caught in two times we have first time no fish and second time he caches a fish gives
0.122×(1-0.122) = 0.1071
 
        
             
        
        
        
Answer:
its 10
Step-by-step explanation:
because all you have to do is add a zero for each place you go