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:
y = 3/4x
Step-by-step explanation:
We need to find the slope of the line
We have point (0,0) and point (4,3)
m = (y2-y1)/(x2-x1)
= (3-0)/(4-0)
=3/4
The y intercept is 0 since it crosses the y axis at 0
The slope intercept form of the line is
y = mx+b
y = 3/4x +0
y = 3/4x
Answer:
125x125
125=5x5x5
125x125=5x5x5x5x5x5=5 to the power of 6
Answer:
147
Step-by-step explanation:
2(X)= (X) x (X)
12 x 12 + 3= 144+3=147
