Q1 Write the following third order ODE as a system of three first order equa- tions d?y dy 2x- + 2y = 2x4. dx? dx Hint: Start by rewriting the equation in the form of y" = F(x, y, y', y'").
Q1 Write the following third order ODE as a system of three first order equa- tions d?y dy 2x- + 2y = 2x4. dx? dx Hint: Start by rewriting the equation in the form of y" = F(x, y, y', y'").
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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![**Q1** Write the following third order ODE as a system of three first order equations
\[ x^3 \frac{d^3 y}{dx^3} + x^2 \frac{d^2 y}{dx^2} - 2x \frac{dy}{dx} + 2y = 2x^4. \]
*Hint: Start by rewriting the equation in the form of \( y''' = F(x, y, y', y'') \).*
**Q2** State one advantage and one disadvantage of implicit methods for solving ODEs.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad10dbe2-69d5-44c1-bbde-1a4f79a6621c%2F6f09ae92-64b7-4a08-aacc-75f5aa12e124%2F4s8osi_processed.png&w=3840&q=75)
Transcribed Image Text:**Q1** Write the following third order ODE as a system of three first order equations
\[ x^3 \frac{d^3 y}{dx^3} + x^2 \frac{d^2 y}{dx^2} - 2x \frac{dy}{dx} + 2y = 2x^4. \]
*Hint: Start by rewriting the equation in the form of \( y''' = F(x, y, y', y'') \).*
**Q2** State one advantage and one disadvantage of implicit methods for solving ODEs.
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