Find the determinant. -K² = (x²)(3x²) - (2x) (x³) w(x³, x²) = The Wronskian is not is not equal to 0 for every x in the interval (0, ∞o), therefore the set of solutions are not are linearly independent. Step 3 We have verified that x² and x³ are linearly independent solutions of the following second-order, homogenous differential equation on the interval (0, 0). x2y" 4xy + 6y= 0 The solutions are called a fundamental set of solutions to the equation, as there are two linearly independent solutions and the equation is second-order. By Theorem 4.1.5, the general solution an equation, in the case of second order, with a fun solutions y₁ and y₂ on an interval is given by the following. Y = C₁Y₁ + C₂Y2 Find the general solution of the given equation.
Find the determinant. -K² = (x²)(3x²) - (2x) (x³) w(x³, x²) = The Wronskian is not is not equal to 0 for every x in the interval (0, ∞o), therefore the set of solutions are not are linearly independent. Step 3 We have verified that x² and x³ are linearly independent solutions of the following second-order, homogenous differential equation on the interval (0, 0). x2y" 4xy + 6y= 0 The solutions are called a fundamental set of solutions to the equation, as there are two linearly independent solutions and the equation is second-order. By Theorem 4.1.5, the general solution an equation, in the case of second order, with a fun solutions y₁ and y₂ on an interval is given by the following. Y = C₁Y₁ + C₂Y2 Find the general solution of the given equation.
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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Transcribed Image Text:Find the determinant.
w(x³, x²) =
x² x3
[1
2x 3x²|
= (x²)(3x²) - (2x) (x³)
The Wronskian is not is not equal to 0 for every x in the interval (0, ∞o), therefore the set of solutions are not
x4
y =
Step 3
We have verified that x² and x³ are linearly independent solutions of the following second-order, homogenous differential equation on the interval (0, ∞).
x2y" 4xy' + 6y = 0
The solutions are called a fundamental set of solutions to the equation, as there are two linearly independent solutions and the equation is second-order. By Theorem 4.1.5, the general solution of an equation, in the case of second order, with a fundamental set of
solutions y₁ and y₂ on an interval is given by the following.
y = C₁Y₁ + C₂Y ₂
Find the general solution of the given equation.
Submit
are linearly independent.
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