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Consider the IVP dealing with nonhomogeneous second order linear differential equation with variable coefficients (x-1)y"(x)-xy'(x) + y(x) = (x-1)² e*, y(0) = 0, y'(0)=0 The functions y₁(x)=x and y₂(x)= e* are independent solutions of the associated homogeneous equation (x-1)y"(x)-xy(x) + y(x) = 0. (a) When using the method of variation of parameters to find a particular solution y(x) of the nonhomogeneous equation in the form y(x)=y₁ (x)v, (x) + y₂(x)₂(x), the functions v, and v₂ satisfy the system of equations OA. xv₁ (x) + e*v₂(x)=0 and v₁ (x) + e*v₂(x)=(x-1) e* OB. xv₁ (x) + e*v₂(x)=(x-1) ex and v₁ (x) + e*v₂(x) = 0 OC. xv₁ (x) + e*v₂(x) = 0 and v₁'(x) + e*v₂'(x) = (x - 1)² ex OD. xv₁'(x) + e*v₂(x) = 0 and v₁'(x) + e*v₂'(x) = (x - 1) ex OE. None of the answers given is correct

Consider the IVP dealing with nonhomogeneous second order linear differential equation with variable coefficients (x-1)y"(x)-xy'(x) + y(x) = (x-1)² e*, y(0) = 0, y'(0)=0 The functions y₁(x)=x and y₂(x)= e* are independent solutions of the associated homogeneous equation (x-1)y"(x)-xy(x) + y(x) = 0. (a) When using the method of variation of parameters to find a particular solution y(x) of the nonhomogeneous equation in the form y(x)=y₁ (x)v, (x) + y₂(x)₂(x), the functions v, and v₂ satisfy the system of equations OA. xv₁ (x) + e*v₂(x)=0 and v₁ (x) + e*v₂(x)=(x-1) e* OB. xv₁ (x) + e*v₂(x)=(x-1) ex and v₁ (x) + e*v₂(x) = 0 OC. xv₁ (x) + e*v₂(x) = 0 and v₁'(x) + e*v₂'(x) = (x - 1)² ex OD. xv₁'(x) + e*v₂(x) = 0 and v₁'(x) + e*v₂'(x) = (x - 1) ex OE. None of the answers given is correct

Advanced Engineering Mathematics
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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Consider the IVP dealing with nonhomogeneous second order linear differential equation with variable coefficients (x-1)y"(x)-xy'(x) + y(x) = (x-1)² e*, y(0) = 0, y'(0)=0 The functions y₁(x)=x and y₂(x)= e* are independent solutions of the associated homogeneous equation (x-1)y"(x)-xy(x) + y(x) = 0. (a) When using the method of variation of parameters to find a particular solution y(x) of the nonhomogeneous equation in the form y(x)=y₁ (x)v, (x) + y₂(x)₂(x), the functions v, and v₂ satisfy the system of equations OA. xv₁ (x) + e*v₂(x)=0 and v₁ (x) + e*v₂(x)=(x-1) ex OB. xv₁ (x) + e*v₂(x) = (x-1) e* and v₁ (x) + e*v₂(x)=0 OC. xv₁ (x) + e*v₂(x) = 0 and v₁'(x) + e*v₂'(x) = (x − 1)² e* OD. xv₁'(x) + e*v₂(x) = 0 and v₁'(x) + e*v₂'(x) = (x - 1) e* OE. None of the answers given is correct
Transcribed Image Text:Consider the IVP dealing with nonhomogeneous second order linear differential equation with variable coefficients (x-1)y"(x)-xy'(x) + y(x) = (x-1)² e*, y(0) = 0, y'(0)=0 The functions y₁(x)=x and y₂(x)= e* are independent solutions of the associated homogeneous equation (x-1)y"(x)-xy(x) + y(x) = 0. (a) When using the method of variation of parameters to find a particular solution y(x) of the nonhomogeneous equation in the form y(x)=y₁ (x)v, (x) + y₂(x)₂(x), the functions v, and v₂ satisfy the system of equations OA. xv₁ (x) + e*v₂(x)=0 and v₁ (x) + e*v₂(x)=(x-1) ex OB. xv₁ (x) + e*v₂(x) = (x-1) e* and v₁ (x) + e*v₂(x)=0 OC. xv₁ (x) + e*v₂(x) = 0 and v₁'(x) + e*v₂'(x) = (x − 1)² e* OD. xv₁'(x) + e*v₂(x) = 0 and v₁'(x) + e*v₂'(x) = (x - 1) e* OE. None of the answers given is correct
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