**Title: Solving a Linear Differential System Using Elimination****Introduction:**This section demonstrates how to use the elimination method to find a general solution for a given linear system with differentiation with respect to $ t $.**Problem Statement:**Solve the following linear system of differential equations:\[2x' + 10y = 0\]\[x' - y' = 0\]**Instructions:**Eliminate variable $ x $ and solve the resulting differential equation for $ y $. Select the correct solution from the options below.**Choices:**- **A.** $ y(t) = C_2 \sin(-5t) $ - **B.** $ y(t) = C_2 \cos(-5t) $ - **C.** $ y(t) = C_2 e^{5t} $ - **D.** $ y(t) = C_2 e^{-5t} $ - **E.** The system is degenerate.**Conclusion:**Apply the elimination method effectively to simplify the system and find the correct general solution for $ y(t) $. Evaluate the options given and identify the valid choice.

Solution : Given 2x1+10y=0 -I x1-y1 =0 -II Multiply equation II by -2…

Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x' + 10y = 0 x' -y' = 0 Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. O A. Y(t) = C2 sin ( – 5t) О В. У) - С2 сos (- 5t) 5t OC. y(t) = C2 e - 5t O D. y(t) = C2 e O E. The system is degenerate.

Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x' + 10y = 0 x' -y' = 0 Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. O A. Y(t) = C2 sin ( – 5t) О В. У) - С2 сos (- 5t) 5t OC. y(t) = C2 e - 5t O D. y(t) = C2 e O E. The system is degenerate.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

**Title: Solving a Linear Differential System Using Elimination**

**Introduction:**
This section demonstrates how to use the elimination method to find a general solution for a given linear system with differentiation with respect to $ t $.

**Problem Statement:**
Solve the following linear system of differential equations:
\[
2x' + 10y = 0
\]
\[
x' - y' = 0
\]

**Instructions:**
Eliminate variable $ x $ and solve the resulting differential equation for $ y $. Select the correct solution from the options below.

**Choices:**

- **A.** $ y(t) = C_2 \sin(-5t) $
- **B.** $ y(t) = C_2 \cos(-5t) $
- **C.** $ y(t) = C_2 e^{5t} $
- **D.** $ y(t) = C_2 e^{-5t} $
- **E.** The system is degenerate.

**Conclusion:**
Apply the elimination method effectively to simplify the system and find the correct general solution for $ y(t) $. Evaluate the options given and identify the valid choice.

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