Please answer the following question showing steps and full details and thank yo
ID: 2852400 • Letter: P
Question
Please answer the following question showing steps and full details and thank you.
Let x and y be functions of the variable t and suppose that they satisfy the coupled differential equations
x ? + 2 y = cos t
y ? ? 2 x = sin t ,
where x? and y? denote the derivatives of x and y with respect to t, and x(0)= y(0)=0.
Set L[x]=u and L[y]=v, where L denotes the Laplace transform. Let s denote the usual variable in the transform space.
1) What equations do u and v satisfy?
2) What is the solutions u and v of the system of equtions in question 1)?
3) Using u and v from Question 2), determine the solutions x(t), y(t) of the coupled differential equations from Question 1).
Table of Laplace Transforms cos(at) s2+a2 sin(at)aExplanation / Answer
Let x and y be functions of the variable t and suppose that they satisfy the coupled differential equations
x + 2 y = cos t
y 2 x = sin t ,
where x and y denote the derivatives of x and y with respect to t, and x(0)=y(0)=0.
Set L[x]=u and L[y]=v, where L denotes the Laplace transform. Let s denote the usual variable in the transform space.
1) What equations do u and v satisfy?
2) What is the solutions u and v of the system of equtions in question 1)?
3) Using u and v from Question 2), determine the solutions x(t), y(t) of the coupled differential equations from Question 1).