Solution Found!
As in Exercises 3.6, for some problems you
Chapter 3, Problem 13E(choose chapter or problem)
The solution to the initial value problem
\(\frac{d y}{d x}=y^{2}-2 e^{x} y+e^{2 x}+e^{x}\), \(y(0)=3\)
has a vertical asymptote ("blows up") at some point in the interval . By experimenting with the fourth-order Runge-Kutta subroutine, determine this point to two decimal places.
Equation Transcription:
Text Transcription:
\frac{d y}{d x}=y^{2}-2 e^{x} y+e^{2 x}+e^{x}
y(0)=3
Questions & Answers
QUESTION:
The solution to the initial value problem
\(\frac{d y}{d x}=y^{2}-2 e^{x} y+e^{2 x}+e^{x}\), \(y(0)=3\)
has a vertical asymptote ("blows up") at some point in the interval . By experimenting with the fourth-order Runge-Kutta subroutine, determine this point to two decimal places.
Equation Transcription:
Text Transcription:
\frac{d y}{d x}=y^{2}-2 e^{x} y+e^{2 x}+e^{x}
y(0)=3
ANSWER:
Solution:-
Step1
Given that
By experimenting with the fourth-order Runge–Kutta subroutine, determine this point to two decimal places.
Step2
We have
The solution to the initial value problem
has a vertical asymptote (“blows up”) at some point in the interval [0,2].
Step3
We know that, the fourth-order Runge kutta subroutine approximation formula is:
Where ,
Step4
Now when n=4
h=
Where b=2 and a=0
x |
y |
0 |
3 |
18.46 |
|
1 |
Therefore, x=1
Step5
when n=8
h=
Where b=2 and a=0