Problem #8: Two linearly independent solutions of xy" -(1+x)y' +y = 0 are y₁(x) = 1 + x and y₂(x) = e. (a) Find the Wronskian W(v₁, 2) of y₁ and 12. (b) Using the method of variation of parameters, we want to find a particular solution yp of the following ODE xy" - (1+x)y' +y = x²e²x in the form y(x) = u₁(x)y₁(x) + u₂(x)y₂(x) for some functions u₁ and u₂. The differential equation for u₂(x) can be written as u₂' =.... Type the right-hand side of this equation into the answer box below. (c) Solve the equation from part (b) to find the function 12.
Problem #8: Two linearly independent solutions of xy" -(1+x)y' +y = 0 are y₁(x) = 1 + x and y₂(x) = e. (a) Find the Wronskian W(v₁, 2) of y₁ and 12. (b) Using the method of variation of parameters, we want to find a particular solution yp of the following ODE xy" - (1+x)y' +y = x²e²x in the form y(x) = u₁(x)y₁(x) + u₂(x)y₂(x) for some functions u₁ and u₂. The differential equation for u₂(x) can be written as u₂' =.... Type the right-hand side of this equation into the answer box below. (c) Solve the equation from part (b) to find the function 12.
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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