Please answer correctly. I need this ASAP please. thank you This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skippedpart.Tutorial ExerciseConsider the differential equationx²y" - 6xy' +10y = 0; x², x5, (0, ∞o).Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval.Form the general solution.Step 1We are given the following homogenous differential equation and pair of solutions on the given interval.x²y" - 6xy' +10y = 0; x², x5, (0, 0)We are asked to verify that the solutions are linearly independent. That is, there do not exist constants c₁ and c₂, not both zero, such that c₁x² + ₂x³ = 0. While this may be clear for these solutionsthat are different powers of x, we have a formal test to verify the linear independence.Recall the definition of the Wronskian for the case of two functions f and f₂, each of which have a first derivative.f₁ f₂f₁ f₂By Theorem 4.1.3, if W(f₁, f₂) = 0 for every x in the interval of the solution, then solutions are linearly independent.Let f₁(x) = x² and f₂(x) = x5. Complete the Wronskian for these functions.|x²+5W(f₁, f₂) =W(x², x5)=2x

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se e differential equation x²y" - 6xy + 10y = 0; x², x³, (0, 00). the given functions form a fundamental set of solutions of the differential equation on the indicated interval. eneral solution. n the following homogenous differential equation and pair of solutions on the given interval. x²y" - 6xy' + 10y = 0; x², x5, (0, ∞) ed to verify that the solutions are linearly independent. That is, there do not exist constants c₁ and c₂, not both zero, such that c₁x² + ₂x³ = 0. While this may be clear for these solutions ferent powers of x, we have a formal test to verify the linear independence. lefinition of the Wronskian for the case of two functions f and f₂, each of which have a first derivative. W(f₂, f₂) = f₁ f₂ f₂f₂ 4.1.3, if W(f₁, f₂) = 0 for every x in the interval of the solution, then solutions are linearly independent. x² and f₂(x) = x³. Complete the Wronskian for these functions. 2x

se e differential equation x²y" - 6xy + 10y = 0; x², x³, (0, 00). the given functions form a fundamental set of solutions of the differential equation on the indicated interval. eneral solution. n the following homogenous differential equation and pair of solutions on the given interval. x²y" - 6xy' + 10y = 0; x², x5, (0, ∞) ed to verify that the solutions are linearly independent. That is, there do not exist constants c₁ and c₂, not both zero, such that c₁x² + ₂x³ = 0. While this may be clear for these solutions ferent powers of x, we have a formal test to verify the linear independence. lefinition of the Wronskian for the case of two functions f and f₂, each of which have a first derivative. W(f₂, f₂) = f₁ f₂ f₂f₂ 4.1.3, if W(f₁, f₂) = 0 for every x in the interval of the solution, then solutions are linearly independent. x² and f₂(x) = x³. Complete the Wronskian for these functions. 2x

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 1CR

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