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y = C1 cos 3x + c2 sin 3x => y" + 9y = 9

y = C1 cos 3x + c2 sin 3x => y" + 9y = 9

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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NOTE: PLEASE ANSWER PART 2 ONLY
PT 2 Directions: Determine whether the given first expression is the solution of the succeeding given ODE. 1. y = c1e²x + c2e-3x => y"+y'-6y=0 2. y c1 cos 3x + c2 sin 3x => y" +9y = 9 3. y = C₁x² + C₂x³ => x²y" - 4xy' + 6y = 0 4. y = C₁ex + c₂e²x + c3e³x => y" - 6y" + 11y' - 6y=0 5. y = C₁ cos (21nx) + c2 sin (21n x) => x²y"+ xy' + 4y = 0
Transcribed Image Text:PT 2 Directions: Determine whether the given first expression is the solution of the succeeding given ODE. 1. y = c1e²x + c2e-3x => y"+y'-6y=0 2. y c1 cos 3x + c2 sin 3x => y" +9y = 9 3. y = C₁x² + C₂x³ => x²y" - 4xy' + 6y = 0 4. y = C₁ex + c₂e²x + c3e³x => y" - 6y" + 11y' - 6y=0 5. y = C₁ cos (21nx) + c2 sin (21n x) => x²y"+ xy' + 4y = 0
Directions: In each of the following problems, assume a, b, c and d are arbitrary constants, determine the equivalent ODE by eliminating the arbitrary constants. 1. y = aex + be³x 2. y = ae²x + be4x 3. x² + axy + bx + c = 0 4. y = aebx 5. ya sin (x + b) 6. y=xsin (x + c) 7. y = ae2x + be³x + x²
Transcribed Image Text:Directions: In each of the following problems, assume a, b, c and d are arbitrary constants, determine the equivalent ODE by eliminating the arbitrary constants. 1. y = aex + be³x 2. y = ae²x + be4x 3. x² + axy + bx + c = 0 4. y = aebx 5. ya sin (x + b) 6. y=xsin (x + c) 7. y = ae2x + be³x + x²
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