In Problems 1 through 16, a homogeneous second-order lin- ear differential equation, two functions y₁ and y2, and a pair of initial conditions are given. First verify that y₁ and y₂ are solutions of the differential equation. Then find a particular solution of the form y = C₁y1 + C2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x. 13. x²y" - 2xy' + 2y = 0; y₁ = x, y2 = x²; y(1) : = 3, y'(1) = 1
In Problems 1 through 16, a homogeneous second-order lin- ear differential equation, two functions y₁ and y2, and a pair of initial conditions are given. First verify that y₁ and y₂ are solutions of the differential equation. Then find a particular solution of the form y = C₁y1 + C2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x. 13. x²y" - 2xy' + 2y = 0; y₁ = x, y2 = x²; y(1) : = 3, y'(1) = 1
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 15CR
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![In Problems 1 through 16, a homogeneous second-order lin-
ear differential equation, two functions y₁ and y2, and a pair
of initial conditions are given. First verify that y₁ and y₂ are
solutions of the differential equation. Then find a particular
solution of the form y = C₁y1 + C2y2 that satisfies the given
initial conditions. Primes denote derivatives with respect to x.
13. x²y" - 2xy' + 2y = 0; y₁ = x, y2 = x²; y(1) : = 3,
y'(1) = 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1f6654a-b208-424e-8549-ae895b2e4de2%2F8d5719d1-9dd3-4076-aec9-584b0aa91671%2Fr2bif1s_processed.png&w=3840&q=75)
Transcribed Image Text:In Problems 1 through 16, a homogeneous second-order lin-
ear differential equation, two functions y₁ and y2, and a pair
of initial conditions are given. First verify that y₁ and y₂ are
solutions of the differential equation. Then find a particular
solution of the form y = C₁y1 + C2y2 that satisfies the given
initial conditions. Primes denote derivatives with respect to x.
13. x²y" - 2xy' + 2y = 0; y₁ = x, y2 = x²; y(1) : = 3,
y'(1) = 1
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