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(1) Use series to find the solution of the differential equation (x²-1)y" + 3xy + xy = 0 with y(0) = 4, y' (0) = 6.

(1) Use series to find the solution of the differential equation (x²-1)y" + 3xy + xy = 0 with y(0) = 4, y' (0) = 6.

Calculus For The Life Sciences
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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(1) Use series to find the solution of the differential equation (x²-1)y"+3xy + xy = 0 with y(0) = 4, y' (0) = 6. (2) Show that L{(1 + ²)²}= (3) For the differential equation 4(s² - 4s+2) s(8-2)(8-4) (a) Separation of variables; (b) Linear equations method; do the following: (a) Show that x = 0 is a regular singular point. (b) Find the indicial equation and the indicial roots of it. (c) Use the Frobenius method to find two series solutions of the equation: (4) Solve the first order differential equation y - 3y = 0 with y(0) = 1 using the following methods: (c) Power series method; and (d) Laplace Transform Method. y 4xy + +y=0 2 (5) Use the Laplace Transform Method to solve the linear equation y" -y - 2y = 4t² with initial conditions y(0) = 1 y' (0) = 4
Transcribed Image Text:(1) Use series to find the solution of the differential equation (x²-1)y"+3xy + xy = 0 with y(0) = 4, y' (0) = 6. (2) Show that L{(1 + ²)²}= (3) For the differential equation 4(s² - 4s+2) s(8-2)(8-4) (a) Separation of variables; (b) Linear equations method; do the following: (a) Show that x = 0 is a regular singular point. (b) Find the indicial equation and the indicial roots of it. (c) Use the Frobenius method to find two series solutions of the equation: (4) Solve the first order differential equation y - 3y = 0 with y(0) = 1 using the following methods: (c) Power series method; and (d) Laplace Transform Method. y 4xy + +y=0 2 (5) Use the Laplace Transform Method to solve the linear equation y" -y - 2y = 4t² with initial conditions y(0) = 1 y' (0) = 4
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