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hree solutions of the ODE x³y"" + 6x²y" + 4xy' - 4y = 0 are y₁ = x, y₂ = x-², and 3 = 3x-² + 8x. Compute the Wronskian of the set {y₁, y2, Y3} to determine if these unctions are linearly independent on the interval (0, ∞o). Based on your result, could you orm the general solution of the ODE by forming the equation y(x) = C₁y₁ + C₂y2 + C3Y3?

hree solutions of the ODE x³y"" + 6x²y" + 4xy' - 4y = 0 are y₁ = x, y₂ = x-², and 3 = 3x-² + 8x. Compute the Wronskian of the set {y₁, y2, Y3} to determine if these unctions are linearly independent on the interval (0, ∞o). Based on your result, could you orm the general solution of the ODE by forming the equation y(x) = C₁y₁ + C₂y2 + C3Y3?

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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Three solutions of the ODE x³y"" + 6x²y" + 4xy' - 4y = 0 are y₁ = x, y₂ = x², and Y3 = 3x-² + 8x. Compute the Wronskian of the set {y₁, y2, Y3} to determine if these functions are linearly independent on the interval (0, ∞). Based on your result, could you form the general solution of the ODE by forming the equation y(x) = C₁y₁ + C₂V2 + C3Y3?
Transcribed Image Text:Three solutions of the ODE x³y"" + 6x²y" + 4xy' - 4y = 0 are y₁ = x, y₂ = x², and Y3 = 3x-² + 8x. Compute the Wronskian of the set {y₁, y2, Y3} to determine if these functions are linearly independent on the interval (0, ∞). Based on your result, could you form the general solution of the ODE by forming the equation y(x) = C₁y₁ + C₂V2 + C3Y3?
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