Need yn for x vaules 0.7 and 1.1 only!
Suppose that we use Euler's method to approximate the solution to the differential equation
(dy)/(dx)=(x^(3))/(y);,y(0.3)=6.
Let f(x,y)=(x^(3))/(y).
We let x_(0)=0.3 and y_(0)=6 and pick a step size h=0.2. Euler's method is the the following
algorithm. From x_(n) and y_(n), our approximations to the solution of the differential equation at the nth
stage, we find the next stage by computing
x_(n+1)=x_(n)+h,y_(n+1)=y_(n)+h*f(x_(n),y_(n)).
Complete the following table. Your answers should be accurate to at least seven decimal places.
The exact solution can also be found using separation of variables. It is
y(x)=
Thus the actual value of the function at the point x=1.3
y(1.3)=
(1 point) Suppose that we use Euler's method to approximate the solution to the differential equation
dy x3 dx y
y(0.3) = 6.
Let f(x,y)=x3/y We let xo = 0.3 and Yo = 6 and pick a step size h = 0.2. Euler's method is the the following algorithm. From xn and yn, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing
Xn+1 = Xn+ h,
Yn+1 =Yn+hf(xn,Yn).
Complete the following table.Your answers should be accurate to at least seven decimal places
Xn 0.3
Yn 6
0
0.5
6.0009
2 0.7
6.003033
0.9
6.01649
1.1
6.05010289
1.3
6.08479
The exact solution can also be found using separation of variables.It is
y(x) = (x^4+71.9919)^(1/2)/(2^(1/2))
Thus the actual value of the function at the point x = 1.3 y(1.3) = 6.117515836
