Solution Found!
In 1 and 2, verify that the pair x (t) , y (t) is a
Chapter 5, Problem 2E(choose chapter or problem)
In Problems 1 and 2, verify that the pair is a solution to the given system. Sketch the trajectory of the given solution in the phase plane.
\(\frac{d x}{d t}=1, \frac{d y}{d t}=3 x^{2}\);
\(x(t)=t+1\) \(y(t)=t^{3}+3 t^{2}+3 t\)
Equation transcription:
Text transcription:
frac{d x}{d t}=1, frac{d y}{d t}=3 x^{2}
x(t)=t+1
y(t)=t^{3}+3 t^{2}+3 t
Questions & Answers
QUESTION:
In Problems 1 and 2, verify that the pair is a solution to the given system. Sketch the trajectory of the given solution in the phase plane.
\(\frac{d x}{d t}=1, \frac{d y}{d t}=3 x^{2}\);
\(x(t)=t+1\) \(y(t)=t^{3}+3 t^{2}+3 t\)
Equation transcription:
Text transcription:
frac{d x}{d t}=1, frac{d y}{d t}=3 x^{2}
x(t)=t+1
y(t)=t^{3}+3 t^{2}+3 t
ANSWER:Solution:
Step 1
In this problem we have to verify that the pair , and
is a solution to the given system.