Find the general solution of the Cauchy-Euler ODES on (0,00).a. 2x²y" +5xy' + y = 0b. x²y" -9xy' + 25y = 0c. x³y"" - 6y=0

Answered: Find the general solution of the…

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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(9) Each of the following ODEs can be made variable separable using a substitution. Give the substitution and show how to obtain a variable separable ODE from this substitution. You have not been asked to solve these equations. (e) (Hand in) = 3+ (2y-x)¹/2 dz
1
Q 6 please
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
ky and k is a nonzero constant, then y could be (A) 2e*y (B) 2e (B) (C) e+3 (D) kty+5 2. OD OB ョ0 O A Question 2 = cos(2x), then y= %3D (A) 2. cos (2x)+C (B) 2. cos (2x) +C (C) 극sin (2x)+C 2. D) 극 1. sin2 (2x)+C 1. (E) --sin (2x)+C 2. 2.
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. 3. x² + axy + bx + c = 0 4. y = aebx 5. ya sin (x + b) 6. y = x sin (x + c) 7. yae2x + be³x + x²
PT 2 Directions: Determine whether the given first expression is the solution of the succeeding given ODE. 1. y 2. y = C1 cos 3x + c2 sin 3x => y" +9y=9 3. y = C1x² + C2x³ => x²y" - 4xy' + 6y = 0 4. y = C₁e* + Cze²x + c3e³x => y" - 6y" + 11y' - 6y = 0 5. y = C₁ cos (21nx) + C₂ sin (2ln x] => x²y"+ xy' + 4y = 0
Consider the ODE: "7y" - +7y=0. Which one of the following is the general solution to this ODE? Ⓒy(x) = ₁² +₂e +ce where c₁,9,R Ⓒy(x) = ₁² + €₂e-² +ce where c,, y(t) = ₁² +₂¹+ce where c₁, c2, y(t) = ₁² +₂e+ce" where ₁,0, R R ER

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Find the general solution of the Cauchy-Euler ODES on (0,00). a. 2x²y" +5xy' + y = 0 b. x²y" -9xy' + 25y = 0 c. x³y"" - 6y=0