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Write the given third order linear equation as an equivalent system of first order equations with initial values. 3 cos(t)y" — y" — 2ty + (3t³ + 2 − 2t²)y = 2 − tª + 3t Use x₁ = y, x2 = y, and x3 = y'. with initial values x If you don't get this in 2 tries, you can get a hint. with y(0) = 3, y'(0) = 1, y'(0) = −3

Write the given third order linear equation as an equivalent system of first order equations with initial values. 3 cos(t)y" — y" — 2ty + (3t³ + 2 − 2t²)y = 2 − tª + 3t Use x₁ = y, x2 = y, and x3 = y'. with initial values x If you don't get this in 2 tries, you can get a hint. with y(0) = 3, y'(0) = 1, y'(0) = −3

Advanced Engineering Mathematics
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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Write the given third order linear equation as an equivalent system of first order equations with initial values. 3 cos (t)y" — y" — 2ty' + (3t³ + 2 − 2t²) y = 2 − tª + 3t - Use x₁ = y, x2 = y', and x3 = y". 18 || = with initial values 8 If you don't get this in 2 tries, you can get a hint. 18 x + with y(0) = 3, y′(0) = 1, y'(0) = −3
Transcribed Image Text:Write the given third order linear equation as an equivalent system of first order equations with initial values. 3 cos (t)y" — y" — 2ty' + (3t³ + 2 − 2t²) y = 2 − tª + 3t - Use x₁ = y, x2 = y', and x3 = y". 18 || = with initial values 8 If you don't get this in 2 tries, you can get a hint. 18 x + with y(0) = 3, y′(0) = 1, y'(0) = −3
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