We want to solve the Initial Value Problem y' = y + 4xy, with y(0) = 1.
To use Euler's method, define
y(i+1) = y(i) + hy'(i), for i=0,1,2, ...,
where
h = 0.1, the step size.,
x(i) = i*h
1st step.
y(0) = 1 (given) and x(0) = 0.
y(1) ≡ y(0.1) = y(0) + h*[4*x(0)*y(0)] = 1
2nd step.
x(1) = 0.1
y(2) ≡ y(0.2) = y(1) + h*[4*x(1)*y(1)] = 1 + 0.1*(4*0.1*1) = 1.04
3rd step.
x(2) = 0.2
y(3) ≡ y(0.3) = y(2) + h*[4*x(2)*y(2)] = 1.04 + 0.1*(4*0.2*1.04) = 1.1232
4th step.
x(3) = 0.3
y(4) ≡ y(0.4) = y(3) + h*[4*x(3)*y(3)] = 1.1232 + 0.1*(4*0.3*1.1232) = 1.258
5th step.
x(4) = 0.4
y(5) ≡ y(0.5) = y(4) + h*[4*x(4)*y(4)] = 1.258 + 0.1*(4*0.4*1.258) = 1.4593
Answer: y(0.5) = 1.4593
Answer:
You use the Pytha. theorem to find the length of the missing side or the hypotenuse
Step-by-step explanation:
a^2 + b^2 = c^2
c^2 = the hypotenuse
Answer:
All real numbers are solutions.
Step-by-step explanation:
![\boxed{\text{The slope is 0.}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Ctext%7BThe%20slope%20is%200.%7D%7D)
Slope is a number that represents how much the y-value changes over a certain span of x-values. However, since y is a constant set to 3, the y-value never changes, meaning the slope is 0.
The slope will always be 0 for any equation that has the form:
![y=\text{some number}](https://tex.z-dn.net/?f=y%3D%5Ctext%7Bsome%20number%7D)
You could also choose two random points and solve for the slope. Let's take (0,3) and (1,3).
You can verify these are actual points on the line since the y-value is 3.
Now, let's calculate for slope:
![\text{Slope}=\dfrac{3-3}{1-0}=\dfrac{0}{1}=0](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D%5Cdfrac%7B3-3%7D%7B1-0%7D%3D%5Cdfrac%7B0%7D%7B1%7D%3D0)
The slope is indeed 0 as shown from this.
Let me know if you need any clarifications, thanks!
~ Padoru
Im confused what do you mena