Just as there are simultaneous algebraic equations (where a pair of numbers have

Question

Just as there are simultaneous algebraic equations (where a pair of numbers have to satisfy a pair of equations) there are systems of differential equations, (where a pair of functions have to satisfy a pair of differential equations). Indicate which pairs of functions satisfy this system. It will take some time to make all of the calculations. y1' = 5/2y1 - 3/2y2 y2' = -3/2y1 + 5/2y2 y1 = ex y2 = ex y1 = 2e-2x y2 = 3e-2x y1 = -ex y2 = e-x y1 = sin(x) y2 = cos(x) y1 = sin(x) + cos(x) y2 = cos(x) - sin(x) y1 = e4x y2 = -e4x y1 = cos(x) y2 = -sin(x) As you can see, finding all of the solutions, particularly of a system of equations, can be complicated and time consuming. It helps greatly if we study the structure of the family of solutions to the equations. Then if we find a few solutions we will be able to predict the rest of the solutions using the structure of the family of solutions.

Explanation / Answer

A. C. E. G.

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.