(1) First verify that yn and 2 are solutions of the following differential equations, then find a particular solution of the form y=ch+2 that satisfies the given initial conditions. Primes denote derivatives with respect to z. (a) y-y=0; -, /2; y(0)-0, y'(0)-5. (b) z²" +2ry-6y=0; -², 2-³; (2)-10, (2) - 15.
(1) First verify that yn and 2 are solutions of the following differential equations, then find a particular solution of the form y=ch+2 that satisfies the given initial conditions. Primes denote derivatives with respect to z. (a) y-y=0; -, /2; y(0)-0, y'(0)-5. (b) z²" +2ry-6y=0; -², 2-³; (2)-10, (2) - 15.
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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HW6P1

Transcribed Image Text:(1) First verify that y₁ and 2 are solutions of the following differential equations, then find a particular solution
of the form y = ₁3/1+022 that satisfies the given initial conditions. Primes denote derivatives with respect
to z.
(a) y - y = 0; h=², 1/₂=²; y(0) = 0, y/'(0) = 5.
(b) x²y" + 2xy-6y=0; ₁=², 1/₂ = ³; (2) = 10, (2) = 15.
(2) Show that 1/1 = ² and 2 = ³ are two solutions of zy" - Ary' +6y= 0, both satisfying the initial
conditions y(0) = 0 ='(0). Explain why these facts do not contradict Theorem 2 (with respect to the
guaranteed uniqueness).
(3) Find the general solutions of the differential equation:
Ay" - 12y +9y=0.
(4) Solve the initial value problem:
(5) Solve the initial value problem:
"-6y +25y=0; y(0) = 3, y(0) = 1.
"+"=0; y(0) = -1, (0) = 0, "(0) = 1.
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(.) If are the solution of a differential equation then satisfy the differential equation .
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